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. In the case of Kuznetsov components of Fano complete intersections, this leads to a proof of a conjecture of Katzarkov and Kontsevich on the dimensions of such categories, and implies the nonexistence of Serre invariant stability conditions when the degrees of the complete intersection do not all coincide. This is joint work with Alexander Kuznetsov.

algebraic geometry

Audience: researchers in the topic

ZAG (Zoom Algebraic Geometry) seminar

Series comments: Description: ZAG seminar

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