Abelian varieties are projective algebraic varieties endowed with an Abelian group structure. Over the complex numbers, they can be described as quotients of a vector space by a lattice of full rank. They are analogs in higher dimensions of elliptic curves, and play an important role in algebraic geometry and number theory.
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Why do people think that abelian varieties are the hardest case for the Hodge conjecture?Why can projective varieties just have abelian group operations?
Why no abelian varieties over Z?
Is there any rational curve on an Abelian variety?
non principally polarized complex abelian varieties
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