Room 509, Cosmology Building, National Taiwan University + Zoom, Physical+Online Seminar
(實體+線上演講 台灣大學次震宇宙館509研討室+ Zoom)
Categorical Torelli Theorems for Fano Threefolds: A Survey
Augustinas Jacovskis (University of Luxembourg)
Abstract
Let X be a smooth Fano threefold. Then its derived category of coherent sheaves D(X) determines it up to isomorphism, by Bondal—Orlov’s reconstruction theorem. Since X is Fano, D(X) admits a non-trivial semiorthogonal decomposition consisting of a number of vector bundles, and the orthogonal to them; a subcategory known as the Kuznetsov component Ku(X). It is a natural question whether Ku(X) determines X up to isomorphism. In this talk, I will survey the (very different) moduli-theoretic and Hodge-theoretic approaches to this problem, which cover most of the 17 deformation classes of smooth Fano threefolds of Picard rank 1.
Organizer: Pedro Núñez (NTU)
