BIMSA > BIMSA AG Seminar BIMSA AG Seminar Stability conditions on derived categories of abelian varieties
Stability conditions on derived categories of abelian varieties
Organizers
Artan Sheshmani , Nanjun Yang , Beihui Yuan
Speaker
Fabien Haiden
Time
Thursday, March 12, 2026 3:00 PM - 4:00 PM
Venue
A6-101
Online
Zoom 638 227 8222 (BIMSA)
Abstract
Describing the full space of stability conditions for the derived category of a projective variety is typically a difficult problem. In the case of a power of an elliptic curve without complex multiplication, Kontsevich gave a conjectural description based on homological mirror symmetry. In joint work with Ben Sung (arXiv:2410.08028) we proved this conjecture in the 3-fold case, where the space of stability conditions has dimension 14. I will report on work in progress to handle the case of elliptic curve with complex multiplication. Their powers form abelian varieties which maximize the rank of the numerical K-group among abelian varieties of the same dimension and are a steppingstone towards the case of general abelian varieties. The description of the space of stability conditions involves passing to the product of the abelian variety and its dual, a technique going back work of Mukai, Orlov, Polishchuk, and others.