K-theoretic Donaldson invariants via instanton counting
Algebraic Geometry
2007-05-23 v1 High Energy Physics - Theory
Differential Geometry
Abstract
In this paper we study the holomorphic Euler characteristics of determinant line bundles on moduli spaces of rank 2 semistable sheaves on an algebraic surface X, which can be viewed as -theoretic versions of the Donaldson invariants. In particular, if X is a smooth projective toric surface, we determine these invariants and their wallcrossing in terms of the K-theoretic version of the Nekrasov partition function (called 5-dimensional supersymmetric Yang-Mills theory compactified on a circle in the physics literature). Using the results of math.AG/0606180 we give an explicit generating function for the wallcrossing of these invariants in terms of elliptic functions and modular forms.
Cite
@article{arxiv.math/0611945,
title = {K-theoretic Donaldson invariants via instanton counting},
author = {Lothar Göttsche and Hiraku Nakajima and Kota Yoshioka},
journal= {arXiv preprint arXiv:math/0611945},
year = {2007}
}
Comments
72 pages, 2 figures