All Questions
7
questions
2
votes
0
answers
274
views
A gap in a proof of Orlov’s result on the group of autoequivalences of the derived category of an abelian variety
Let $X$ be an abelian variety over an algebraically closed field of charactristic $0$. In this paper, Orlov showed that there is a short exact sequence $$0\to \mathbb Z \oplus X \times \hat X \to\...
- 256
4
votes
0
answers
291
views
Derived categories of coherent sheaves and degenerations of abelian varieties
By the work of Burban-Drozd (https://projecteuclid.org/euclid.dmj/1076621984), we know what happens to the derived category of coherent sheaves when an elliptic curve degenerates into a nodal curve or ...
- 3,157
2
votes
0
answers
223
views
What are the point-like objects in $D^b(X)$ when $X$ is an abelian variety?
Let $X$ be a projective variety over an algebraically closed field $k$ and $D^b(X)$ be the derived category of bounded complexes of coherent sheaves on $X$. Let $S$ be the Serre functor on $D^b(X)$. ...
- 8,767
1
vote
1
answer
212
views
Derived equivalence of families of dual abelian varieties
Let $B$ be a smooth projective complex variety and $\pi:X\to B$ a smooth projective map whose fibres $X_b$ are abelian varieties. Let $\psi:Y\to B$ be the naturally associated bundle such that the ...
- 3,007
0
votes
0
answers
247
views
Hodge structure of abelian surfaces
In my case, I have an abelian surface $A$ of (2,8)-polarization, and I have some finite group (may not be abelian group) $G$ acting on $A$ without fixed point. I want to understand when there is a ...
- 3,392
5
votes
1
answer
916
views
Fourier-Mukai transform for abelian varieties
Let $A$ be an abelian variety over $\mathbb{C}$, $L$ be a very ample line bundle on $A$, then the dual abelian variety is $\hat{A} \cong A/K(L)$ with $K(L)$ the kernel of surjective morphism $A \to ...
- 3,392
2
votes
1
answer
448
views
Could we construct the Jacobian variety of a smooth curve $C$ with genus $>2$ from its derived category $D(C)$?
Let's consider a smooth curve $C$ over $\mathbb{C}$. We know that the Jacobian variety $Jac(C)$ of $C$ is the moduli space of the degree $0$ line bundles on $C$. $Jac(C)$ is an abelian variety of ...
- 8,767