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# Degenerations of Hilbert schemes of points

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Lars Halle (Copenhagen)

What SFB-Kolloquium Jun 30, 2016 from 03:30 pm to 04:30 pm Mainz, 05-432 (Hilbertraum) vCal iCal

Abstract.

Let $C$ be a smooth curve and $f : X \to C$ a simple degeneration with smooth fibers away from a point $0 \in C$. I will present a "good" compactification of the relative Hilbert scheme of points associated to the smooth locus of $f$. This compactification is obtained by GIT-methods, and gives a new, alternative, approach to earlier constructions of J. Li and B. Wu.

I will focus on the case where $f$ is a degeneration of surfaces, and explain how this set-up can be used to study degenerations of irreducible holomorphic symplectic varieties. This is joint work with M. Gulbrandsen and K. Hulek.