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# Dr. Xuqiang Qin, UNC-CH – Birational geometry of Beauville-Mukai systems on K3 surfaces

## October 7, 2022 @ 4:00 pm - 5:00 pm

Mode: In-person

Title: Birational geometry of Beauville-Mukai systems on K3 surfaces

Abstract: *A Beauville-Mukai system on a K3 surface is a moduli space of stable torsion sheaves, which admits a Lagrangian fibration given by mapping each sheaf to its support. In this talk, we will focus on a class of Beauville-Mukai systems which are birational to Hilbert schemes of points on the surface. Using wall-crossing techniques from Bridgeland stability, we decompose the birational map into a sequence of flops, whose exceptional loci are Brill-Noether type subsets. As a result, we give full description of the birational geometry of such systems. This is based on joint work with Justin Sawon.*