Serre functors of semiorthogonal components

Abstract: The Serre functor of a triangulated category is one of its most important invariants, playing the role of the dualizing complex of a variety in noncommutative algebraic geometry. I will explain how to describe the Serre functors of many semiorthogonal components of varieties in terms of spherical twists, with applications to a dimension formula for Kuznetsov components of complete intersections conjectured by Katzarkov and Kontsevich, to the nonexistence of Serre invariant stability conditions, and to the construction of Calabi-Yau categories as crepant contractions. This is joint work with Alexander Kuznetsov.

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)