EQUIVARIANT MODULI THEORY ON K3 SURFACES
Dr. Yuhang Chen
2023-06-13 14:00-15:00
MCM110
Speaker: Dr. Yuhang Chen (Ohio State University)Time: 14:00-15:00 June 13, 2023 (Tuesday)
Place: MCM110
Title: EQUIVARIANT MODULI THEORY ON K3 SURFACES
Abstract: In this talk, I will define equivatiant moduli spaces of stable sheaves on a projective scheme under an action of a finite group. Let X be a K3 surface, and let G be a finite subgroup G of the symplectic automorphism group of X. I will use the orbifold HRR formula to compute the dimensions of G-equivariant moduli spaces of stable sheaves on X under the action of the finite group G. I will then apply the orbifold HRR formula to reproduce the number of fixed points on X when G is cyclic without using the Lefschetz fixed point formula. I will prove that under some mild conditions, equivariant moduli spaces of stable sheaves on X are irreducible symplectic manifolds deformation equivalent to Hilbert schemes of points on X via a connection between Gieseker and Bridgeland moduli spaces, as well as the derived McKay correspondence. As a corollary, these moduli spaces are also deformation equivalent to G-equivariant Hilbert schemes of points on X.
