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Results tagged with abelian-varieties
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user 450
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.
31
votes
Is there any rational curve on an Abelian variety?
Over $\mathbb C$ you can argue as follows.
Suppose you have a morphism $\mathbb P^1(\mathbb C) \to A $ ($A$= abelian variety ). Since $\mathbb P^1(\mathbb C) $ is simply connected , the morphism l …
- 47.5k
11
votes
Accepted
Explicit way to construct simple complex tori/abelian varieties of dimension at least 2
Recall that the Néron-Severi group of a complex manifold $X$ is the subgroup of $NS(X)\subset H^2(X, \mathbb Z) $ consisting of first Chern classes of holomorphic line bundles on $X$.
More algebraical …
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