\(K\)-theoretic Donaldson invariants via instanton counting
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Publication:2390742
DOI10.4310/PAMQ.2009.V5.N3.A5zbMATH Open1192.14011arXivmath/0611945OpenAlexW2964295938MaRDI QIDQ2390742
Author name not available (Why is that?)
Publication date: 3 August 2009
Published in: (Search for Journal in Brave)
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.
Full work available at URL: https://arxiv.org/abs/math/0611945
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