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Results tagged with abelian-varieties
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user 51424
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.
22
votes
Accepted
Which hypersurfaces in $\mathbb{P}^n$ are abelian varieties?
Really this is mostly just consolidating what has been (implicitly) said in the comments and cleaning it up a bit (e.g. using the Chow ring instead of singular cohomology), but might as well make it a …
- 5,958
1
vote
Accepted
Lifting of automorphism of rational surface to that on abelian variety
Denote $X\backslash\text{Sing}(X)$ by $X_0$ and its preimage in $Y$ as $Y_0$. Note that $Y_0$ is the Galois cover of $X_0$ corresponding to the normal subgroup $\mathbb{Z}[i]\times\mathbb{Z}[i]$ insid …
- 5,958
6
votes
Accepted
$K_0$-equivalence of varieties
(Expanding my comments into an answer for more visibility.)
By Larsen-Lunts $K_0(\operatorname{Var}_k)/[\mathbb{A}^1]$ is the free abelian group on stable birational equivalence classes. It thus suff …
- 5,958