Euler characteristics of Hilbert schemes of points on simple surface singularities

Author: 

Gyenge, Á
Némethi, A
Szendroi, B

Publication Date: 

26 March 2018

Journal: 

European Journal of Mathematics

Last Updated: 

2020-10-05T07:11:04.15+01:00

Issue: 

2

Volume: 

4

DOI: 

10.1007/s40879-018-0222-4

page: 

439-524

abstract: 

We study the geometry and topology of Hilbert schemes of points on the orbifold surface [C2/G], respectively the singular quotient surface C2/G, where G < SL(2, C) is a finite subgroup of type A or D. We give a decomposition of the (equivariant) Hilbert scheme of the orbifold into affine space strata indexed by a certain combinatorial set, the set of Young walls. The generating series of Euler characteristics of Hilbert schemes of points of the singular surface of type A or D is computed in terms of an explicit formula involving a specialized character of the basic representation of the corresponding affine Lie algebra; we conjecture that the same result holds also in type E. Our results are consistent with known results in type A, and are new for type D.

Symplectic id: 

822888

Submitted to ORA: 

Submitted

Publication Type: 

Journal Article