wiktionary varieties varietyVariety may refer to tocright Mathematics Abelian variety , a complex torus that can be embedded into projective space Abstract variety , an intrinsically defined variety Algebraic variety , the basic object of study in algebraic geometry Algebraic variety Affine variety , a subset of algebraic varieties Algebraic variety Projective variety , a subset of algebraic varieties Quasiprojective variety , a subset of algebraic varieties which includes projective and affine varieties Analytic variety , an object much like an algebraic variety but defined as the zero set of finitely many real or complex analytic functions Variety universal algebra , classes of algebraic structures defined by equations in universal algebra Sciences Variety botany , a formal rank in botanical taxonomic nomenclature Variety cybernetics , the number of possible states of a system or of an element of the system Varietylinguistics , a concept that includes, for instance, dialects, standard language and jargon Plant variety law , a legal rather than taxonomic term for a cultivar or hybrid protected by patent law Variety , an informal and incorrect and ambiguous rather than taxonomic term for cultivar in horticulture Arts and entertainment Broadcast media Variety US radio , a format of radio programming Variety show , a form of theatrical and television entertainment Film Variet , a 1925 silent film Variety Girl , a 1947 all star movie musical produced by Paramount Pictures Variety ... tabloid size magazine Variety from 1907 to 1996 Variety 1983 film , a 1983 film Hobbies Variety, a term in coin collecting see Glossary of numismatics VarietyVariety philately , a term in stamp collecting Music Variety Les Rita Mitsouko album Variety Les Rita Mitsouko album , the seventh studio album by Les Rita Mitsouko Variety Tokyo Incidents album Variety Tokyo Incidents album , Japanese band Tokyo Jihen s third studio album Variety Playhouse , music venue in the Little Five Points neighborhood ... more details
In mathematics the meaning of variety can be in algebraic geometry , an algebraic variety , which may be affine, projective or abstract or in universal algebra , a variety universal algebra variety , a set of structures satisfying some further given set of equations on their elements. mathdab ... more details
In mathematics, the Kummer variety of an abelian variety is its quotient by the map taking any element to its inverse. The Kummer variety of a 2 dimensional abelian variety is called a Kummer surface . References Citation last1 Shimura first1 Goro title Abelian varieties with complex multiplication and modular functions publisher Princeton University Press series Princeton Mathematical Series isbn 978 0 691 01656 6 id MathSciNet id 1492449 year 1998 volume 46 Category Abelian varieties ... more details
In algebraic geometry, a Severi variety , named after Francesco Severi , may be a Brauer Severi variety a variety contained in a Hilbert scheme that parametrizes curves in projective space with given degree, arithmetic genus, and number of nodes and no other singularities. a Scorza variety of dimension n in projective space of dimension 3 n 2 2 that can be isomorphically projected to a hyperplane. mathdab ... more details
Unreferenced stub auto yes date December 2009 Orphan date October 2008 A composite variety is a plant population in which at least 70 of its Progeny genetic descendant progeny result from the cross breeding crossing of the parent lines. DEFAULTSORT Composite Variety Category Plant reproduction Category Agriculture stubs Botany stub Composite variety is a variety developed by mixing the seeds of various phenotypically outstanding lines possessing similarities for various characteristics like height, seed size, seed color, maturity etc. Crossing among the selected is encouraged. Features of Composite Variety Heterogeneous Relevant to cross pollinated species only Can be developed from open pollinated variety any other heterozygous variety Farmer can use his own saved seed for 3 to 4 years, after that seed should be replaced There can be two or more constituent genotypes Evaluation for general combining ability gca as in synthetic variety production, is not carried out Exact reconstitution of composite variety is not possible Examples and development of composite variety are given on the page Composite Variety Production. Visit to know more on the topics. ... more details
In mathematics, a ruled variety is a variety birational to a product of the projective line and another variety, and a uniruled variety is a variety that is dominated by a ruled variety. This concept is a generalisation not too remote of the ruled surface s of classical differential geometry. A variety is uniruled if and only if there is a rational curve passing though every point. Any uniruled variety has Kodaira dimension &minus &infin . In dimension at most 3, and conjecturally in all dimensions, the converse is true a variety of Kodaira dimension &minus &infin is uniruled. Consequences of the Miyaoka Mori theorem for smooth varieties Let X be a smooth projective variety over an algebraically closed field and math mathcal K X math its canonical divisor . Then if there exists a curve C in X such that math C . mathcal K X 0 math , the variety X is ruled. In particular, if X has nef line bundle nef anticanonical divisor , then for X to be ruled, it suffices for the anticanonical divisor to not be numerically trivial. References Citation last1 Clemens first1 Herbert last2 Koll r first2 J nos last3 Mori first3 Shigefumi title Higher dimensional complex geometry id MathSciNet id 1004926 year 1988 journal Ast risque issn 0303 1179 issue 166 pages 144 pp. 1989 Category algebraic geometry ... more details
Plant variety may refer to Variety botany , a taxonomic nomenclature rank in botany, below subspecies, but above subvariety and form Plant variety law , a non taxonomic, exclusively legal term applied to plants for which patent protection has been applied or to which it applies taxonomic categorization of such a plant may, on a case by case basis, be any Infraspecies infraspecific rank , usually a cultivar or hybrid Variety , an informal, incorrect and ambiguous substitute for form botany , a taxonomic nomenclature rank in botany, below variety as formally defined at variety botany and subvariety but above subform Variety , an informal, incorrect, ambiguous and vague substitute for cultivar or hybrid biology , the lowest taxonomic nomenclature ranks in botany used especially with regard to grapes and rice the equivalent term varietal , though not an official botany term, is also common in horticulture generally and is not as ambiguous, although still vague disambig id Varietas ... more details
Unreferenced date January 2010 About the taxonomic rank in botany Variety disambiguation In botanical nomenclature , variety abbreviated var. in Latin varietas is a taxonomic rank below that of species as such, it gets a three part Infraspecific name botany infraspecific name . Botanical nomenclature A variety will have an appearance distinct from other varieties, but will hybridize freely with those other varieties if brought into contact . Usually varieties will be geographically separate from each other. Example The pincushion cactus, Escobaria vivipara Nutt. Buxb., is a wide ranging variable species occurring from Canada to Mexico , and found throughout New Mexico below about convert 2600 m ft . Nine varieties have been described. Where the varieties of the pincushion cactus meet, they intergrade . The variety Escobaria vivipara var. arizonica is from Arizona , while Escobaria vivipara var. neo mexicana is from New Mexico. Other nomenclature uses In plant breeding nomenclature, at least in countries that are signatory to the UPOV Convention, variety plant variety or plant variety ... . A name that was published before 1961 as that of a variety is taken to be the name of a subspecies. A name published after 1960 as that of a variety does not formally exist. In zoology, Form ... Code of Zoological Nomenclature ICZN . In bacteriological nomenclature variety is not allowed ... nomenclature, what is referred to as grape variety grape varieties are in reality cultivar s according to usage in the International Code of Nomenclature for Cultivated Plants or variety plant ... seed plant s . However, usage of the term variety is so entrenched in viticulture that a change to cultivar is unlikely. Plant variety law Subvariety Variety plant See also Trinomial nomenclature Form ... Variety Category Plant taxonomy 1rank26 botany stub ar az M xt liflik botanika ca Varietat ... botanica pl Odmiana biologia pt Variedade biologia simple Variety botany sk Odroda sv Varietet botanik ... more details
Variety Tonight was a CBC Radio show which aired from 1980 until 1984 at 8 10 PM. Variety Tonight was a nightly series featuring jazz music jazz and pop music as well as trivia game s, book and movie review s and interviews . The show was hosted by David Coles radio host David Coles 1980 81 followed by Vicki Gabereau . External links http www.broadcasting history.ca networks CBC Radio Program Details VARIETY TONIGHT.html Variety Tonight Category CBC Radio One programs Canada radio show stub ... more details
In mathematics , a norm variety is a particular type of algebraic variety V over a field mathematics field F , introduced for the purposes of algebraic K theory by Voevodsky . The idea is to relate Milnor K theory of F to geometric objects V , having function field of an algebraic variety function field s F V that split given symbols elements of Milnor K groups . The formulation is that p is a given prime number, different from the characteristic algebra characteristic of F , and a symbol is the class mod p of an element math a 1, dots, a n math of the n th Milnor K group. A field extension is said to split the symbol, if its image in the K group for that field is 0. The conditions on a norm variety V are that V is irreducible and a non singular complete variety . Further it should have dimension of an algebraic variety dimension d equal to math p n 1 1. math The key condition is in terms of the d th Newton polynomial s sub d sub , evaluated on the algebraic total Chern class of the tangent bundle of V . This number math s d V math should not be divisible by p sup 2 sup , it being known it is divisible by p . Examples These include n 2 cases of the Severi Brauer variety and p 2 Pfister form s. There is an existence theorem in the general case paper of Markus Rost cited . External links http www.math.uni bielefeld.de rost data nv ac.pdf Paper by Rost Category Algebraic varieties Category K theory ... more details
Infobox magazine title Variety image file Variety logo sm.jpg image size 200px president Neil R Stiles ... variety.com issn 0042 2738 Variety is an American weekly entertainment trade journal trade magazine ... motion picture industry , Daily Variety , a daily edition based in Los Angeles, was founded by Silverman in 1933. In 1998, the Daily Variety Gotham edition, based in New York City was added. All three have been in continual operation since. Now delivered to 60 countries, Variety presents in depth ... production charts, an in depth industry calendar and reviews dating back to 1914. Variety Events target every aspect of the entertainment industry. These events include the Variety Screening Series, held in both NYC and LA showcasing award contenders and Variety s philanthropic Power of events, including Power of Youth, Power of Women, Power of Comedy, and Power of Music. Variety also delivers ... of Reed Elsevier . History Variety has been published since December 16, 1905, ref cite news ... launched Daily Variety , based in Hollywood, Los Angeles, California Hollywood . Silverman was the editor of the Variety Inc. publications until selecting Abel Green as his replacement in 1931 he remained ..., was the sole heir to what was then Variety Inc. Young Syd s legal guardian Harold Erichs oversaw Variety Inc. until 1956. From then Syd took over and managed the company until 1987, when he sold it to Cahners ... of vice president and editorial director , characterised online as Boffo No More Bart Up and Out at Variety ... of Guard at Variety Reflects Shifting Landscape work The New York Times date April 6, 2009 Accessed ... Editorial Editorial Staff . Variety . Undated. Accessed August 9, 2009. ref Circulation Paid circulation is currently 61,144 across Daily Variety, weekly Variety, and Variety.com, representing ... . Editions Variety started in 1905 is a glossy Tabloid newspaper format tabloid edition with a broad .... It is published weekly and delivered internationally. Daily Variety started in 1933 is the name of the Los ... more details
In mathematics , a quasiprojective variety in algebraic geometry is a locally closed subset of a projective variety , i.e., the intersection inside some projective space of a Zariski open and a Zariski closed subset. A similar definition is used in scheme theory , where a quasiprojective scheme is a locally closed subscheme of some projective space. ref http eom.springer.de q q076660.htm ref Relationship to affine varieties For example, affine space is a Zariski open subset of projective space , and since any closed affine subset math U math can be expressed as an intersection of the projective completion math bar U math and the affine space embedded in the projective space, this implies that any affine variety is quasiprojective. There are locally closed subsets of projective space that are not affine, so that quasiprojective is more general than affine. Taking the complement of a single point in projective space of dimension at least 2 gives a non affine quasiprojective variety. This is also an example of a quasiprojective variety that is neither affine nor projective. Examples Since quasiprojective varieties generalize both affine and projective varieties, they are sometimes referred to simply as varieties . Varieties isomorphic to affine algebraic varieties as quasiprojective varieties are called affine variety affine varieties similarly for projective varieties. For example, the complement of a point in the affine line, i.e. math X mathbb A 1 0 math , is isomorphic to the zero set of the polynomial math xy 1 math in the affine plane. As an affine set X is not closed since any polynomial zero on the complement must be zero on the affine line. For another example, the complement ... that a manifold is locally Euclidean &mdash every point of a quasiprojective variety has a neighborhood given by an affine variety. This yields a basis of affine sets for the Zariski topology on a quasiprojective variety. References Igor R. Shafarevich, Basic Algebraic Geometry 1 , Springer ... more details
In mathematics , the Albanese variety A V , named for Giacomo Albanese , is a generalization of the Jacobian variety of a curve, and is the abelian variety generated by a variety V taking a given point of V to the identity of A . In other words there is a morphism from the variety V to its Albanese variety A V , such that any morphism from V to an abelian variety taking the given point to the identity factors uniquely through A V . For complex manifolds harvtxt Blanchard 1956 defined the Albanese variety in a similar way, as a morphism from V to a torus A V such that any morphism to a torus factors uniquely through this map. Although it is called a variety in this case, it need not be algebraic. For compact space compact K hler manifold s the dimension of the Albanese is the Hodge number h sup 1,0 sup , the dimension of the space of differentials of the first kind on V , which for surfaces is called the irregularity of a surface . In terms of differential form s, any holomorphic 1 form on V is a pullback differential geometry pullback of an invariant 1 form on the Albanese, coming from the holomorphic cotangent space of Alb V at its identity element. Just as for the curve case, by choice of a base point on V from which to integrate , an Albanese morphism math V to operatorname Alb V math is defined, along which the 1 forms pull back. This morphism is unique up to a translation on the Albanese. For varieties over fields of positive characteristic, the dimension of the Albanese variety may be less than the Hodge numbers h sup 1,0 sup and h sup 0,1 sup which need not be equal . Connection to Picard variety The Albanese variety is duality theory of abelian varieties dual to the Picard variety the connected space connected component of zero of the Picard scheme classifying invertible sheaves on V math operatorname Alb ,V operatorname Pic 0 ,V vee math For algebraic curves, the Abel ... Wiley Interscience year 1994 isbn 0 471 05059 8 pages 331, 552 eom id Albanese variety first A. N ... more details
The New Variety was a Chicago based cabaret produced by Thom Goodman and Richard O Donnell in the 1990s. It was a fast paced, ever changing volley of acts that included award winning jugglers , fire eaters, stand up comedy , singers, musicians, and sketch comedy troupes. History In February 1992, producers Thom Goodman founder, CrossCurrents and Richard O Donnell founder, New Age Vaudeville teamed up to present the New Variety, located at 400 N. Clark, downtown Chicago . ref name Kogan citation periodical Chicago Tribune, Arts, Pg 2, Section 13 date March 1, 1992 title New Variety takes its first steps first Rick last Kogan ref Modeled after the vaudeville variety shows of the 20s and 30s, the New Variety presented an evening s worth of acts that included jugglers, fire eaters, comics, singers, musicians, and sketch comedy troupes. ref name Helbig citation periodical New City, Arts date July 23, 1992 title The New Variety first Jack last Helbig ref It was hailed by the Chicago Tribune as a Cabaret for the 90s. ref name Sawyers citation periodical Chicago Tribune, Friday, Page 2 Section 7 date May 15, 1992 title New Variety a cabaret for the 90s first June last Sawyers ref The bill included artistic director & host Richard O Donnell billed as R. , jazz band the Vince Willis Trio, juggler ... July 2, 1992 title New Variety Cabaret Features a Wealth of Entertainment first Elaine last Belsito ref Barbara LeShoure. Improv Comedy Club In August, 1993, the New Variety moved to the Chicago Improv ... August 6, 1993 title Improv Adds Some Variety To Its Stage first Ernest last Tucker ref and was responsible for changing a faltering 3 ring comedy presentation into a successful variety format. The New Variety now offered a more streamlined, commercial show. ref name Adler citation periodical Chicago Tribune, Overnight date May 27, 1993 title New Variety Offers Slicker Mix in New Digs first Tony ... New Variety Category American comedy troupes Category Theatre companies in Chicago, Illinois ... more details
refimprove date June 2011 A variety show , also known as variety arts or variety entertainment , is an entertainment made up of a variety of acts hence the name , especially musical performances and sketch ..., acrobatics , juggling and ventriloquism . The variety format made its way from Victorian era stage to radio to television. Variety shows were a staple of English language anglophone television from its early days into the 1970s, and lasted into the 1980s. In several parts of the world, variety TV ... Television in the United States 283603 Variety shows?anchor ref1053883 Television in the United States. Encyclop dia Britannica Online, 2011. Web. 06 Jun. 2011 . ref Variety in the UK evolved in theatres ... on British television and radio did an apprenticeship either in stage variety, or during World War II in Entertainments National Service Association ENSA . In the UK, the ultimate accolade for a variety ... sound movies , then radio, and then television shows, including variety shows. In the 1960s, even a popular rock band such as The Beatles undertook this ritual of appearing on variety shows on TV ... the television variety show format with Your Show of Shows 1950 54 and Caesar s Hour 1954 57 . ref ... costume in a similar fashion. On television, variety reached its peak during the period of the 1960s ... Wall or The Muppet Show . Even The Brady Bunch had a variety show. Variety shows were once as common ... modern times reality shows. During the 1960s and 1970s, there were also numerous one time variety ... , none of whom ever had a regular television series. Contemporary U.S. variety shows Variety shows began to fade from popularity in the early 1970s, when research began to show that variety shows appealed ... purge , several of the early era variety shows were canceled, though newer ones fewer in number nonetheless continued to be created and aired for several years after. By the late 1970s, variety shows had mostly ended production, and by the early 1980s, the few new variety shows being produced were ... more details
In mathematics , the Jacobian variety J C of a non singular algebraic curve C of genus mathematics genus g is the moduli space of degree 0 line bundle s. It is the connected component of the identity in the Picard group of C , hence an abelian variety . Introduction The Jacobian variety is named after Carl Gustav Jacobi , who proved the complete version Abel Jacobi theorem , making the injectivity statement of Niels Abel into an isomorphism. It is a principally polarized abelian variety , of dimension g , and hence, over the complex numbers, it is a complex torus . If p is a point of C , then the curve C can be mapped to a subvariety of J with the given point p mapping to the identity of J , and C generates J as a Group mathematics group . Construction over for complex curves Over the complex numbers, the Jacobian variety can be realized as the quotient space V L , where V is the dual of the vector space of all global holomorphic differentials on C and L is the lattice of all elements of V of the form math omega mapsto int gamma omega math where is a closed path topology path in C . The Jacobian of a curve over an arbitrary field was constructed by harvtxt Weil 1948 as part of his proof of the Riemann hypothesis for curves over a finite field. The Abel Jacobi theorem states that the torus thus built is a variety, the classical Jacobian of a curve, that indeed parametrizes the degree 0 line bundles, that is, it can be identified with its Picard variety of degree 0 divisors modulo ... varieties are the Jacobians of curves. The Picard variety , the Albanese variety , and intermediate ... dimension the construction of the Jacobian variety as a quotient of the space of holomorphic 1 forms generalizes to give the Albanese variety , but in general this need not be isomorphic to the Picard variety. References cite book author P. Griffiths authorlink Phillip Griffiths coauthors Joe ... variety Cite book last1 Weil first1 Andr author1 link Andr Weil title Vari t s ab liennes et courbes ... more details
In cybernetics the term variety denotes the total number of distinct states of a system . Overview The term Variety was introduced by W. Ross Ashby to denote the count of the total number of states of a system ... by his Law of Requisite Variety. Ashby says ref Ashby 1956 p 124 ref blockquote Thus, if the order ... only three distinct elements a, b, c. Such a set will be said to have a variety of three elements ... if the variety is to be well defined. ref Ashby 1956 p125 ref blockquote Variety can be stated as an integer ... p126 ref The Law of Requisite Variety If a system is to be stable the number of states of its control ... states the Law as only variety can destroy variety . ref Ashby 1956 p207 ref He sees this as aiding ... with the case of incessant fluctuations or noise. The Requisite Variety condition can be seen as a simple ... equilibrium . Stafford Beer defines variety as the total number of possible states of a system ... s entropy formula Wahrscheinlichkeit . Beer restates the Law of Requisite Variety as Variety absorbs variety . ref Beer 1979 p286 ref Stated more simply the logarithmic measure of variety represents ... of the required inputs and outputs is established then encoder encoded with the minimum variety ... the variety of teams competing in games like football or rugby to produce goals or tries. A winning chess player might be said to have more variety than his losing opponent. Here a simple order group theory ordering is implied. The attenuation and Amplifier amplification of variety were major ... examples. The application of natural and analogue signals to variety analysis require an of estimate ... the patient. Here no amount of variety recording the patients average temperature would detect ... variety see Algedonic alerts in the Viable System Model or VSM . Beer s work in management cybernetics and VSM is largely based on variety engineering. Further applications involving Ashby s view ... and Cellular automaton . Requisite Variety can be seen in Chaitin s Algorithmic information ... more details
In mathematics, an arithmetic variety is the quotient space of a Hermitian symmetric space by an arithmetic subgroup of the associated algebraic Lie group . Further reading Introduction to modern number theory , By Yu I. Manin, Alekse A. Panchishkin On arithmetic varieties by David Kazhdan, Israel J. Math. 44 1983 , no. 2, 139 159. See also Arakelov theory Arithmetic Chow groups Arithmetic Chow groups Arithmetic of abelian varieties Abelian variety Category Number theory algebra stub ... more details
In algebraic geometry, a chordal variety of a variety is the union of all the chords lines meeting 2 points , including the limiting cases of tangent lines. References Citation last1 Griffiths first1 Phillip author1 link Phillip Griffiths last2 Harris first2 Joseph author2 link Joe Harris mathematician title Principles of algebraic geometry publisher John Wiley & Sons location New York series Wiley Classics Library isbn 978 0 471 05059 9 id MathSciNet id 1288523 year 1994 Category Algebraic geometry ... more details
For other varieties named after Coble, see Coble curve , Coble surface , Coble hypersurface . In mathematics, Coble variety is a 4 dimensional variety studied by Arthur Coble . The Coble variety is the moduli space of ordered sets of 6 points in the projective plane, and can be represented as a double cover of the projective 4 space branched over the Igusa quartic . References Citation last1 Hunt first1 Bruce title The geometry of some special arithmetic quotients publisher Springer Verlag location Berlin, New York series Lecture Notes in Mathematics isbn 978 3 540 61795 2 doi 10.1007 BFb0094399 mr 1438547 year 1996 volume 1637 Category Algebraic varieties ... more details
variety is a Algebraic variety Projective variety projective algebraic variety that is also ... for much research on other topics in algebraic geometry and number theory. An abelian variety can be defined by equations having coefficients in any field mathematics field the variety is then said ... appear naturally as Jacobian variety Jacobian varieties the connected components of zero in Picard variety Picard varieties and Albanese variety Albanese varieties of other algebraic varieties. The group law of an abelian variety is necessarily commutative and the variety is non singular . An elliptic curve is an abelian variety of dimension 1. Abelian varieties have Kodaira dimension 0. History ... glimpse of an abelian variety of dimension 2 an abelian surface what would now be called the Jacobian ... of complex tori. He also appears to be the first to use the name abelian variety . It was Andr ... in the study of Hamiltonian system s , and in algebraic geometry especially Picard variety Picard varieties and Albanese variety Albanese varieties . Analytic theory Definition A complex torus ... group lattice of rank 2 g . A complex abelian variety of dimension g is a complex torus of dimension g that is also a projective algebraic variety over the field of complex numbers. Since they are complex ... the structure of an algebraic variety, this structure is necessarily unique. In the case g 1, the notion of abelian variety is the same as that of elliptic curve , and every complex torus gives rise to such a curve for g 1 it has been known since Bernhard Riemann Riemann that the algebraic variety ... by Riemann decides whether or not a given complex torus is an abelian variety, i.e. whether or not it can ... is a complex vector space of dimension g and L is a lattice in V . Then X is an abelian variety if and only ... variety J of dimension g , by means of an analytic map of C into J . As a torus, J carries ... variety J is called the Jacobian variety of C , for any non singular curve C over the complex numbers ... more details
In mathematics , in the field of algebraic geometry , the idea of abstract variety is to define a concept of algebraic variety in an intrinsic way. This followed the trend in the definition of manifold independent of any ambient space Hassler Whitney , in the 1930s by some years, the first notions being those of Oscar Zariski and Andr Weil in the 1940s. It was Weil, in his foundational work, who gave a first acceptable definition of algebraic variety that stood outside projective space . The simplest notion of algebraic variety is affine algebraic variety. If k is a given algebraically closed field, then A sup n sup k is the n fold Cartesian product of k with itself. Given an ideal I in the ring k x sub 1 sub ,...,x sub n sub of polynomials in n variables over k, the zero set V I is the affine variety defined by the ideal. Unfortunately, affine varieties lack a fundamental property known as completeness. To address this deficiency, affine varieties can be completed , by embedding them in projective space. Formally, a new variable x sub 0 sub is introduced, and the polynomials are replaced by homogeneous polynomials. Choosing an index i to omit from the defining polynomials provide an affine subspace of P sup n sup , and an open affine subvariety of the projective variety. The problem with this approach is that the mechanics of working with projective space and homogeneous coordinates is not terribly geometrical, and is also somewhat arbitrary. Taking a step back, we see that if V is projective variety, the set of affine varieties we have defined is an open cover of V. Moreover, if U sub sub is an element of the open cover, there is an associated affine coordinate ring O ... as the structure sheaf . An abstract variety V,O is a topological space V with an associated ... U such that V sub U sub , O sub U sub is isomorphic to an affine variety, and such that any morphism ... The notion of abstract variety is closely analogous to that of a scheme mathematics scheme ... more details
This article is about algebraic varieties. For the term variety of algebras , and an explanation of the difference between a variety of algebras and an algebraic variety, see variety universal algebra . Image Twisted cubic curve.png 200px thumb The twisted cubic is a projective algebraic variety. In mathematics ... s. Algebraic sets are sometimes also called algebraic varieties , but normally an algebraic variety ... variety is employed in the sense which is similar to that of manifold the difference is that a variety may have singular point of an algebraic variety singular points , while a manifold may not. In the Romance ... variety . Proven around the year 1800, the fundamental theorem of algebra establishes a link between ... topology Algebraic varieties can be classed into four kinds affine varieties, quasi affine variety quasi affine varieties , projective varieties, and quasi projective variety quasi projective varieties . There is also the more general notion of an abstract algebraic variety . The above information .... An irreducible affine algebraic set is also called an affine variety . Many authors use the phrase affine variety to refer to any affine algebraic set, irreducible or not this article will use the stricter ... Projective variety Projective varieties Let k be an algebraically closed field and let P sup n sup ... variety . Projective varieties are also equipped with the Zariski topology by declaring all algebraic .... Examples Affine algebraic variety Example 1 Let k be the field of complex numbers C . Let A sup 2 ... subsets. Thus it is an affine algebraic variety. Example 2 Let again k be the field of complex ... algebraic set V is a variety if and only if I V is a prime ideal equivalently, V is a variety if and only ... of each other . Let k V be the coordinate ring of the variety V . Then the dimension of V is the transcendence ... are required. The modern notion of a variety is considerably more abstract than the one above, though equivalent in the case of varieties over algebraically closed fields. An abstract algebraic variety ... more details
Infobox television show name Viva Variety image genre Sketch comedy br Variety show Variety runtime 22 minutes creator Robert Ben Garant br Thomas Lennon actor and screenwriter Thomas Lennon br Michael Ian Black executive producer Kent Alterman br Paul Miller br Jim Sharp starring Thomas Lennon br Kerri Kenney br Michael Ian Black theme music composer Glen Roven country United States language English language English first aired Start date 1997 04 01 last aired End date 1999 12 01 status Ended network Comedy Central related The State TV series The State Viva Variety is an American sketch comedy series that aired on Comedy Central from April 1997 to December 1999. The series satirizes European variety show s. Overview The show stars Thomas Lennon actor and screenwriter Thomas Lennon as Meredith Laupin, Kerri Kenney as the former Mrs. Agatha Laupin, and Michael Ian Black as your cool ass pal Johnny Blue Jeans. In addition to comedy sketches, the show featured musical guests and various performers, including Ben Stiller . Periodically, a troupe of women called The Swimsuit Squad would dance much like the Fly Girls on In Living Color . The show s premise was derived from a sketch from The State TV series The State called The Mr. and Former Mrs. Laupin Variety Program , and the show featured many people who were a part of the comedy troupe. Sketches Though Mr. Laupin, the former Mrs. Laupin, and Johnny Blue Jeans were themselves characters, the show did not utilize recurring characters ... 29, 2011 at the Eureka Theatre in San Francisco, California a two show reunion of Viva Variety ... and Black reunited for a live, on stage performance of Viva Variety , with a guest appearance by State ... can. External links imdb title id 0132665 title Viva Variety tv.com 7224 Viva Variety http sfsketchfest.com performers index autoselect.php?performer vivavariety.jpg Viva Variety at the SF Sketchfest ... television series Category American sketch comedy television shows Category American variety ... more details
In Algebraic Geometry , the Zariski closure of the union of the secant line s to an embedded projective variety math X subset mathbb P n math is the first secant variety to math X math . It is usually denoted math Sigma 1 math . The math k th math secant variety is the Zariski closure of the union of the linear spaces spanned by collections of k 1 points on math X math . It is usually denoted math Sigma k math . Unless math Sigma k mathbb P n math , it is always singular along math Sigma k 1 math , but may have other singular points. If math X math has dimension d, the dimension of math Sigma k math is at most kd d k. References Joe Harris, Algebraic Geometry, A First Course , 1992 Springer Verlag, New York. ISBN 0 387 97716 3 Category Algebraic geometry algebra stub geometry stub ... more details
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