Kuznetsov components of derived categories and constructions of stability conditions on them


Tzu-Yang Chou (University of Edinburgh, UK)
2022-12-22  13:30 - 14:30
Room 440, Astronomy and Mathematics Building

In this talk, I will first focus on the case of smooth Fano threefolds and introduce the concept of Kuznetsov components, defined by the orthogonal complement of some (not full) exceptional collections of vector bundles on the varieties. Given an appropriate exceptional collection of X, the Kuznetsov component Ku(X) can capture the geometry of X itself or even its moduli spaces. For example, there is a so-called derived Torelli theorem: the Kuznetsov component of a cubic threefold determines itself. I will introduce a general method to induce from Bridgeland stability conditions on a triangulated category to stability on its semiorthogonal components by A. Bayer et al. In particular, this gives us a way to prove the existence of Bridgeland stability conditions on Kuznetsov component providing that a Bogomolov-Gieseker type inequality holds.