Euler characteristics of Hilbert schemes of points on surfaces with simple singularities

Author: 

Szendroi, B
Gyenge, A
Nemethi, A

Publication Date: 

1 July 2016

Journal: 

International Mathematics Research Notices

Last Updated: 

2020-10-04T14:54:37.81+01:00

Issue: 

13

Volume: 

2017

DOI: 

10.1093/imrn/rnw139

page: 

4152-4159

abstract: 

This is an announcement of conjectures and results concerning the generating series of Euler characteristics of Hilbert schemes of points on surfaces with simple (Kleinian) singularities. For a quotient surface C^2/G with G < SL(2, C) a finite subgroup, we conjecture a formula for this generating series in terms of Lie-theoretic data, which is compatible with existing results for type A singularities. We announce a proof of our conjecture for singularities of type D. The generating series in our conjecture can be seen as a specialized character of the basic representation of the corresponding (extended) affine Lie algebra; we discuss possible representation-theoretic consequences of this fact. Our results, respectively conjectures, imply the modularity of the generating function for surfaces with type A and type D, respectively arbitrary, simple singularities, confirming predictions of S-duality.

Symplectic id: 

631086

Submitted to ORA: 

Submitted

Publication Type: 

Journal Article