- Jacobian variety
mathematics, the Jacobian variety of a non-singular algebraic curve"C" of genus "g ≥ 1" is a particular abelian variety"J", of dimension"g". The curve "C" is a subvarietyof "J", and generates "J" as a group.
Analytically, it can be realized as the
quotient space"V"/"L", where "V" is the vector spaceof all
theoremregarding Jacobian varieties is Abel's theorem.
*cite conference | author=J.S. Milne | title=Jacobian Varieties | booktitle=Arithmetic Geometry |publisher=Springer-Verlag|location=New York| year=1986 | pages=pp. 167-212|id=ISBN 0-387-96311-1
Wikimedia Foundation. 2010.
Look at other dictionaries:
Jacobian — In vector calculus, the Jacobian is shorthand for either the Jacobian matrix or its determinant, the Jacobian determinant. In algebraic geometry the Jacobian of a curve means the Jacobian variety: a group variety associated to the curve, in which … Wikipedia
Abelian variety — In mathematics, particularly in algebraic geometry, complex analysis and number theory, an Abelian variety is a projective algebraic variety that is at the same time an algebraic group, i.e., has a group law that can be defined by regular… … Wikipedia
Generalized Jacobian — In algebraic geometry = In mathematics, there are several notions of generalized Jacobians, which are algebraic groups or complex manifolds that are in some sense analogous to the Jacobian variety of an algebraic curve, or related to the Albanese … Wikipedia
Prym variety — In mathematics, the Prym variety construction is a method in algebraic geometry of making an abelian variety from a morphism of algebraic curves. In its original form, it was applied to an unramified double covering of a Riemann surface, and was… … Wikipedia
Dual abelian variety — In mathematics, a dual abelian variety can be defined from an abelian variety A, defined over a field K. Contents 1 Definition 2 History 3 Dual isogeny (elliptic curve case) … Wikipedia
Albanese variety — In mathematics, the Albanese variety is a construction of algebraic geometry, which for an algebraic variety V solves a universal problem for morphisms of V into abelian varieties; it is the abelianization of a variety, and expresses abelian… … Wikipedia
Rational variety — In mathematics, a rational variety is an algebraic variety, over a given field K, which is birationally equivalent to projective space of some dimension over K. This is a question on its function field: is it up to isomorphism the field of all… … Wikipedia
Determinantal variety — In algebraic geometry, determinantal varieties are spaces of matrices with a given upper bound on their ranks. Their significance comes from the fact that many examples in algebraic geometry are of this form, such as the Segre embedding of a… … Wikipedia
Séminaire Nicolas Bourbaki (1950–1959) — Continuation of the Séminaire Nicolas Bourbaki programme, for the 1950s. 1950/51 series *33 Armand Borel, Sous groupes compacts maximaux des groupes de Lie, d après Cartan, Iwasawa et Mostow (maximal compact subgroups) *34 Henri Cartan, Espaces… … Wikipedia
Étale cohomology — In mathematics, the étale cohomology groups of an algebraic variety or scheme are algebraic analogues of the usual cohomology groups with finite coefficients of a topological space, introduced by Grothendieck in order to prove the Weil… … Wikipedia