EVENT DETAILS AND ABSTRACT

Title: New perspective on categorical Torelli problems for del Pezzo threefold
Speaker: Shizhuo Zhang
Speaker Info: Max Planck Institute, Bonn
Brief Description:
Special Note:
Abstract:

Let Y be a del Pezzo threefold of Picard rank one and degree d\geq 2. We provide a Brill-Noether reconstruction of those del Pezzo threefolds as a subscheme of a Bridgeland moduli spaces in their Kuznetsov components. We show that any exact equivalence between their Kuznetsov components preserves a distinguished object up to some natural auto-equivalences of the Kuznetsov component. As a result, we give a uniform proof of categorical Torelli theorem for them. Further more, we compute the group of auto-equivalences of their Kuznetsov component by extending the exact equivalences to the whole bounded derived categories. If time permits I will also talk about the group of auto-equivalences of Kuznetsov component of index one prime Fano threefold where a different techniques are used. As an application we show that the group of automorphism of index one genus 8 prime Fano threefold is isomorphic to that of associated Phaffian cubic threefold, which is not known in the literature.