SIMIS Seminar on Algebraic Geometry: Instanton sheaves, fiber of (categorical) period map and Bridgeland moduli space

报告人： Shizhuo Zhang (IBS-CGP, South Korea)

摘要： Let Y be a smooth del Pezzo threefold of degree d, an instanton sheaf E on Y is a rank two stable sheaf such that certain cohomology vanishing condition is satisfied. The locus of instanton bundles on a smooth cubic threefolds parametrized all index one degree 14 prime Fano threefolds sharing the same intermediate Jacobians. In my talk I will first give a Bridgeland moduli theoretical construction of moduli space of instanton sheaves on cubic threefolds. Then I will identify the fiber of the (categorical) period map for a smooth and proper subcategory of Kuznetsov components of a 1-nodal maximally non-factorial prime Fano threefold of degree 14 with the locus of Bridgeland stable objects which are not locally free. Then I will generalize this identification to other genus. Finally I will propose a conjectural identification of the fiber of categorical period map for at most 1-nodal Fano threefolds with Bridgeland moduli spaces in Kuznetsov components of del Pezzo threefolds. If time allows, I will talk about an interesting application: Kuznetsov’s conjecture on jumping lines for instanton bundles.

时间： 10:00-11:00 a.m., Thursday, Dec.12, 2024

地点： Room 1410, SIMIS, Block A, No. 657 Songhu Road, Yangpu District, Shanghai