In mathematics , the Prymvariety construction named for Friedrich Prym is a method in algebraic geometry of making an abelian variety from a morphism of algebraic curve s. In its original form, it was applied to an unramified Double cover topology double covering of a Riemann surface , and was used by Friedrich Schottky F. Schottky and H. W. E. Jung in relation with the Schottky problem , as it now called, of characterising Jacobian varieties among abelian varieties. It is said to have appeared first in the late work of Bernhard Riemann Riemann , and was extensively studied by Wilhelm Wirtinger Wirtinger in 1895, including degenerate cases. Given a non constant morphism &phi C sub 1 sub &rarr C sub 2 sub of algebraic curves, write J sub i sub for the Jacobian variety of C sub i sub . Then from construct the corresponding morphism &psi J sub 1 sub &rarr J sub 2 sub , which can be defined on a divisor class D of degree zero by applying to each point of the divisor. This is a well defined morphism, often called the norm homomorphism . Then the Prymvariety of is the kernel algebra kernel of . To qualify that somewhat, to get an abelian variety , the connected component of the identity of the reduced scheme underlying the kernel scheme theory kernel may be intended. Or in other words take the largest abelian subvariety of J sub 1 sub , on which is trivial. The theory of Prym varieties was dormant for a long time, until revived by David Mumford around 1970. It now plays a substantial role in some contemporary theories, for example of the Kadomtsev Petviashvili equation . One advantage of the method is that it allows one to apply the theory of curves to the study of a wider ... p.p.a.v. s of dimension 3 are not generally Jacobians, but all p.p.a.v. s of dimension 5 or less are Prym ... Complex Abelian Varieties chapter Prym varieties location New York publisher Springer Verlag isbn 3540204881 ... id MR 0379510 year 1974 chapter Prym varieties. I pages 325 350 Category Algebraic curves Category Abelian ... more details
for the mathematician Friedrich Prym The William Prym GmbH & Co. Kommanditgesellschaft KG is the oldest family business in Germany . The holding company is located in Stolberg Rhineland , the main shareholder is currently Michael Dominic Prym. History Refimprove date July 2007 For twelve generations the Prym family has been operating from the city of Stolberg Germany , making and marketing semi finished copper and brass products as well as Haberdasher haberdashery . In the 17th and 18th century they contributed ... to the press fastener, already invented in 1885. Prym and Prym s Zukunft Prym s future became the earliest ... regarding the Prym brand name. His marriage to Russian born Olga G tschow 1884 1975 in 1903 produced ... Prym of America, Inc. , while Axel 1907 89 and Dieter 1917 held leading positions in the Stolberg ... subsidiaries both in Germany and abroad Prym Consumer sewing and needlework accessories , Prym ... today members of the Prym family are still involved in the management of the business. The family stands for continuity in the development of this group of companies. Current In these days Prym produces ... links http www.prym.com Die Holding Wiliam Prym GmbH & Co. KG http www.prym fashion.de Die Prym Fashion GmbH & Co. KG http www.inovan.de Die Inovan GmbH & Co. KG http www.prym consumer.de Die Prym ... Prym Bruck Of flowers, ores, and family ties , in Metal, publ. 11, 1992, pp. 1168 73 Andrea Prym Bruck Ed. I need you 100 Jahre Prym s Druckknopf , Begleitband zur gleichnamigen Ausstellung in Aachen 2003. Prym, Stolberg 2003, ISBN 3 00 011603 6 Joachim Kornelius, Bernd van Boeckel, Erwin Otto Ed. Fingerh te der William Prym Werke die Geschichte einer alten Fingerhutproduktion mit Bildern des ... Willems Prym, Geschichte und Genealogie , Verlag Guido Pressler, Wiesbaden, 1968. Sources Updated ..., P5997a, Andrea Prym Bruck William Prym company archives Justus Hashagen Geschichte der Familie Hoesch ... Prym eo Prym ja ksh Preem ... more details
Friedrich Emil Fritz Prym 28 September 1841 D ren 15 December 1915 Bonn was a German mathematician who introduced Prym varieties and Prym differential s. References Citation last1 Krazer first1 Adolf title Friedrich Prym url http gdz.sub.uni goettingen.de en dms load img ?PPN PPN37721857X 0025&DMDID DMDLOG 0005 language German year 1917 journal Jahresbericht der Deutschen Mathematiker Vereinigung issn 0012 0456 pages 1 25 MathGenealogy id 51693 External links http gdz.sub.uni goettingen.de en dms load img ?PPN GDZPPN002125110 Picture of Prym http www.didaktik.mathematik.uni wuerzburg.de history mathematik prymlebensbild.html Friedrich Prym Category German mathematicians de Friedrich Prym ... more details
In mathematics, a Prym differential of a Riemann surface is a differential form on the universal covering space that transforms according to some complex character mathematics character of the fundamental group . Equivalently it is a section of a certain line bundle on the Riemann surface in the same component as the canonical bundle . Prym differentials were introduced by harvs txt authorlink Friedrich Prym last Prym year 1869 . The space of Prym differentials on a compact Riemann surface of genus g has dimension g 1, unless the character of the fundamental group is trivial, in which case Prym differentials are the same as ordinary differentials and form a space of dimension g . References Citation last1 Prym first1 F.E. title Zur Integration der gleichzeitigen Differentialgleichungen . url http resolver.sub.uni goettingen.de purl?GDZPPN002154129 year 1869 journal Journal f r die reine und angewandte Mathematik issn 0075 4102 volume 70 pages 354 362 Citation last1 Weyl first1 Hermann author1 link Hermann Weyl title The Concept of a Riemann Surface publisher Addison Wesley year 1964 Category Riemann surfaces ... more details
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 Variety linguistics , 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
Good & Evil Paulo Coelho DEFAULTSORT Devil and Miss Prym Category 2000 novels Category Novels ... cs bel a sle na Chantal es El demonio y la se orita Prym it Il diavolo e la signorina Prym ... no Djevelen og fr ken Prym pl Demon i Panna Prym pt O Dem nio e a Srta. Prym ru sv Dj vulen och fr ken Prym ... 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
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