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Results tagged with abelian-varieties
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user 605
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.
7
votes
Quotients of Abelian varieties by finite groups
The quotients of abelian surfaces (over $\mathbb C$) by finite groups are classified by Yoshihara. In particular he determines the possible Kodaira dimensions.
For instance, if the holonomy part of th …
- 2,821
24
votes
3
answers
3k
views
Products of primitive roots of the unity
Let $m>2$ be an integer and $k=\varphi(m)$ be the number of $m$-th primitive roots of the unity. Let $\Phi = \{ \xi_1, \ldots, \xi_{k/2}\} $ be a set of $k/2$ pairwise distinct primitive $m$-th roots …
- 105k
16
votes
Is there any rational curve on an Abelian variety?
Yes, an abelian variety $A$ contains no rational curves.
Suppose not and let $f: \mathbb P^1 \to A$ be a non-constant morphism.
If $f$ is inseparable then it must be the composition of some power …
- 8,828