Abelian variety

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In algebraic geometry an Abelian variety A over a field K is a projective variety, together with a marked point 0 and two algebraic maps: addition A^2\to A and inverse A\to A, such that these two maps, and the point 0 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.

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