S-duality for surfaces with $A_n$-type singularities
Algebraic Geometry
2013-12-23 v2
Abstract
We show that the generating series of Euler characteristics of Hilbert schemes of points on any algebraic surface with at worst -type singularities is described by the theta series determined by integer valued positive definite quadratic forms and the Dedekind eta function. In particular it is a Fourier development of a meromorphic modular form with possibly half integer weight. The key ingredient is to apply the flop transformation formula of Donaldson-Thomas type invariants counting two dimensional torsion sheaves on 3-folds proved in the author's previous paper.
Cite
@article{arxiv.1312.2300,
title = {S-duality for surfaces with $A_n$-type singularities},
author = {Yukinobu Toda},
journal= {arXiv preprint arXiv:1312.2300},
year = {2013}
}
Comments
17 pages. arXiv admin note: text overlap with arXiv:1311.7476