The Topology of Equivariant Hilbert Schemes

2015/12/17 by Bejleri, Dori, Zaimi, Gjergji · 1 citation
#Algebraic Geometry (math.AG) #Combinatorics (math.CO) #FOS: Mathematics

paper · doi:10.48550/arxiv.1512.05774

Abstract

For G a finite group acting linearly on \mathbbA², the equivariant Hilbert scheme Hilb^r[\mathbbA²/G] is a natural resolution of singularities of Sym^r(\mathbbA²/G). In this paper we study the topology of Hilb^r[\mathbbA²/G] for abelian G and how it depends on the group G. We prove that the topological invariants of Hilb^r[\mathbbA²/G] are periodic or quasipolynomial in the order of the group G as G varies over certain families of abelian subgroups of GL₂. This is done by using the Bialynicki-Birula decomposition to compute topological invariants in terms of the combinatorics of a certain set of partitions.

Cited by

• From Hitchin Systems to Rational Elliptic Surfaces with C*-actions via Orbifold Hilbert Schemes

Related

• G-invariant Hilbert Schemes on Abelian Surfaces and Enumerative Geometry of the Orbifold Kummer Surface
• How to calculate A-Hilb C³
• Extended McKay correspondence for quotient surface singularities
• Invariant Hilbert scheme resolution of Popov's SL(2)-varieties I: the toric case
• Euler characteristics of Hilbert schemes of points on simple surface\n singularities