30th October 2019: The Białynicki-Birula decomposition with a view towards singularities

Speaker: Magdalena Zielenkiewicz (University of Warsaw)

Title: The Białynicki-Birula decomposition with a view towards singularities.

Abstract:

For a scheme with an action of the multiplicative group I will introduce the Białynicki-Birula decomposition and discuss the range of situations where it applies and its consequences. I will sketch how it can be used to study the Chow rings of schemes with torus action via localization theory. I will qickly review the Goresky-Kottwitz-MacPherson theory for varieties with finitely many torus fixed points and finitely many invariant curves, and show on the example of the Hilbert scheme of points how the BB-decomposition can be used to remove the finite curves assumption from the GKM theorem. This will also relate the BB-cells to the multigraded Hilbert scheme of Haiman-Sturmfels.

Villa Battelle, Wednesday 30th October, 14:00