Seminar| Institute of Mathematical Sciences
Time: Thursday, January 15th, 2026,15:30-16:30
Location: RS408, IMS
Speaker: Shizhuo Zhang, Sun Yat-sen University
Abstract: A classical result states that a smooth index one prime Fano threefold of degree 14 is uniquely determined by the (geometrically) corresponding cubic threefold and an instanton bundle on it. As a result, the fiber of period map for such a Fano threefold is the locus of rank two instanton bundles on the cubic threefold. In my talk, I will give a categorical re-interpretation of this result and show that such an index one prime Fano threefold is uniquely determined by its Kuznetsov component--a subcategory of bounded derived category and a distinguished object. Then I will talk about its generalization in two directions: smooth Fano threefolds of other genus and nodal Fano threefolds. For the first case, acyclic extension of instanton bundles will appear, for the second case, non-locally free instanton sheaves appear. Then I will describe a correspondence between degeneration of instanton bundles and degeration of smooth Fano threefolds. This is based on a joint work with Zhiyu Liu, Jacovskis Augustinas and a very recent work with Xun Lin and Daniele Faenzi.