Abelian variety: Difference between revisions
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In [[algebraic geometry]] an '''Abelian variety''' <math>A</math> over a [[field]] <math>K</math> is a projective variety, together with a marked point <math>0</math> and two [[algebraic maps]]: addition <math>A^2\to A</math> and inverse <math>A\to A</math>, such that these two maps, and the point <math>0</math> satisfy the [[Abelian group]] axioms. One dimensional Abelian varieties are [[elliptic curves]]. Over the [[complex numbers]] Abelian varieties are | In [[algebraic geometry]] an '''Abelian variety''' <math>A</math> over a [[field]] <math>K</math> is a projective variety, together with a marked point <math>0</math> and two [[algebraic maps]]: addition <math>A^2\to A</math> and inverse <math>A\to A</math>, such that these two maps, and the point <math>0</math> satisfy the [[Abelian group]] axioms. One dimensional Abelian varieties are [[elliptic curves]]. Over the [[complex numbers]] Abelian varieties are a subset of the set of complex [[torus|tori]]. | ||
Revision as of 01:26, 16 December 2008
In algebraic geometry an Abelian variety over a field is a projective variety, together with a marked point and two algebraic maps: addition and inverse , such that these two maps, and the point satisfy the Abelian group axioms. One dimensional Abelian varieties are elliptic curves. Over the complex numbers Abelian varieties are a subset of the set of complex tori.
