K-theoretic Donaldson invariants via instanton counting

Details K-theoretic Donaldson invariants via instanton counting K-theoretic Donaldson invariants via instanton counting

2006-11-30

arxiv.org/abs/math/0611945v1

Mathematics

Algebraic Geometry

72 pages, 2 figures

Scientific paper

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 $K$-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.

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