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Instanton counting and donaldson invariants

Lothar Gottsche International Centre for Theoretical Physics Hiraku Nakajima Kyoto University, Kyoto 606-8502 Kota Yoshioka Department of Mathematics

Differential Geometry mathscidoc:1609.10084

Journal of Differential Geometry, 80, (3), 343-390, 2008
For a smooth projective toric surface we determine the Donaldson invariants and their wallcrossing in terms of the Nekrasov partition function. Using the solution of the Nekrasov conjecture [33, 38, 3] and its refinement [34], we apply this result to give a generating function for the wallcrossing of Donaldson invariants of good walls of simply connected projective surfaces with b+ = 1 in terms of modular forms. This formula was proved earlier in [19] more generally for simply connected 4-manifolds with b+ = 1, as- suming the Kotschick-Morgan conjecture, and it was also derived by physical arguments in [31].
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@inproceedings{lothar2008instanton,
  title={INSTANTON COUNTING AND DONALDSON INVARIANTS},
  author={Lothar Gottsche, Hiraku Nakajima, and Kota Yoshioka},
  url={http://archive.ymsc.tsinghua.edu.cn/pacm_paperurl/20160909135909482080741},
  booktitle={Journal of Differential Geometry},
  volume={80},
  number={3},
  pages={343-390},
  year={2008},
}
Lothar Gottsche, Hiraku Nakajima, and Kota Yoshioka. INSTANTON COUNTING AND DONALDSON INVARIANTS. 2008. Vol. 80. In Journal of Differential Geometry. pp.343-390. http://archive.ymsc.tsinghua.edu.cn/pacm_paperurl/20160909135909482080741.
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