Brill-Noether Reconstruction for Fano Threefolds and Applications

Explore a 32-minute lecture on Brill-Noether reconstruction for Fano threefolds and its applications. Delve into the Kuznetsov component, a natural subcategory of the derived category of Fano threefolds. Learn about the Brill-Noether reconstruction theorem for a series of Fano threefolds, utilizing Bridgeland moduli spaces in Kuznetsov components. Discover the applications of this theorem, including a uniform proof of categorical Torelli theorems for del Pezzo threefolds of degree greater than 1. Gain insights into the complete description of auto-equivalences of Kuznetsov components for several Fano threefolds. This advanced mathematical talk, presented by Zhiyu Liu at the Hausdorff Center for Mathematics, offers a deep dive into cutting-edge research in algebraic geometry and derived categories.