Window categories and wall crossing

Abstract: The D-equivalence conjecture, due to Bondal, Orlov, and Kawamata, predicts that a birational equivalence between smooth projective varieties that preserves the canonical bundle should induce an equivalence of derived categories of coherent sheaves. I will give an overview of "window categories" in equivariant derived categories of coherent sheaves, which can be used to construct derived equivalences for birational transformations coming from variation of GIT quotient. I will then discuss how these were used recently to prove the D-equivalence conjecture for projective Calabi-Yau manifolds in the birational equivalence class of a moduli space of sheaves on a K3 surface.

algebraic geometry

Audience: researchers in the topic

Derived seminar

Series comments: https://ed-ac-uk.zoom.us/j/89993982042

Password: a simply-connected two-dimensional variety with trivial canonical bundle (omit the space)