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 as subset of the set of complex tori. | 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 as subset of the set of complex tori. | ||
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Revision as of 14:48, 9 March 2007
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 as subset of the set of complex tori.
