Degenerations of Hilbert schemes of points on K3 surfaces

Abstract: It is a widely open problem to understand the degenerations of higher dimensional hyperkähler manifolds. The simplest case would be the degenerations of Hilbert schemes of points on K3 surfaces. Given a simple degeneration family of K3 surfaces, there are two existing constructions of the degenerations of the Hilbert schemes of its fibers in the literature, due to Nagai and Gulbrandsen-Halle-Hulek respectively. I will compare the two constructions with an emphasis on the geometry of the latter. Based on joint work with M.G.Gulbrandsen, L.H.Halle and K.Hulek.

algebraic geometryalgebraic topologycomplex variablesdifferential geometrygeometric topologysymplectic geometry

Audience: researchers in the topic

2021 Pacific Rim Complex & Symplectic Geometry Conference