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K-theoretic Donaldson Invariants Via Instanton Counting

2009; Volume: 5; Issue: 3 Linguagem: Inglês

10.4310/pamq.2009.v5.n3.a5

1558-8602

Lothar Göttsche, Hiraku Nakajima, Kōta Yoshioka,

Advanced Algebra and Geometry

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 [43] we give an explicit generating function for the wallcrossing of these invariants in terms of elliptic functions and modular forms.