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Results tagged with abelian-varieties
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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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What is the closure of product loci in A_g?
Let $A_g$ denote the moduli space of principally polarized abelian varieties of dimension $g$. For any partition of $g$, one can consider the corresponding locus inside $A_g$ of products of lower-dime …
- 40.3k
9
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Has anyone studied the Prym map for double covers with two ramification points?
If $f \colon C \to C'$ is a dominant morphism of smooth projective curves, there is a norm map $f_\ast = \mathrm{Nm} \colon JC \to JC'$ between their Jacobians, and we can consider the abelian subvari …
- 40.3k
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Compactifying the space of indecomposable abelian varieties
Let $A_g$ be the moduli space of principally polarized abelian varieties and $A_g^0$ the open substack of indecomposable ones. Abstractly we know $A_g^0$ has a compactification with complement a norma …
- 40.3k
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A frustrating cohomology class on the moduli of abelian surfaces
Here's a very frustrating question that I have been stuck on for some time. I believe that my question could fit in a general framework of what happens when you restrict $L^2$-cohomology classes on a …
- 40.3k