Degenerations of Hilbert schemes of points
Lars Halle (Copenhagen)
What 


When 
Jun 30, 2016 from 03:30 pm to 04:30 pm 
Where  Mainz, 05432 (Hilbertraum) 
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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 GITmethods, 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 setup can be used to study degenerations of irreducible holomorphic symplectic varieties. This is joint work with M. Gulbrandsen and K. Hulek.