K-theoretic Donaldson invariants via instanton counting
arXiv:math/0611945
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.
72 pages, 2 figures
References in corpus (8)
- Geometric Engineering of Quantum Field Theories
- Instantons and recursion relations in N=2 Susy gauge theory
- On the Cobordism Class of the Hilbert Scheme of a Surface
- Four-Dimensional Avatars of Two-Dimensional RCFT
- Seiberg-Witten Theory and Random Partitions
- Instanton sums and five-dimensional gauge theories
- Theta Functions for $\SL(n)$ versus $\GL(n)$
- A note on Fourier-Mukai transform