# Jørgen Rennemo: Fix-point loci in Hilbert schemes of points in the plane

**Time: **
Wed 2019-08-28 13.15 - 15.00

**Location: **
Room 3418, KTH

**Participating: **
Jørgen Rennemo (Oslo)

Abstract: The Betti numbers of Hilbert schemes of points in the plane were first computed by Ellingsrud and Strømme, using Białynicki-Birula's decomposition theorem. In this talk, we consider the following variation: Let a finite cyclic group act strictly non-symplectically on the plane, and compute the Betti numbers of the fix-point locus of the associated action on the Hilbert scheme. The answer is surprisingly nice. Joint work with Paul Johnson.