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November 2008 Instanton counting and Donaldson invariants
Lothar Göttsche, Hiraku Nakajima, Kōta Yoshioka
J. Differential Geom. 80(3): 343-390 (November 2008). DOI: 10.4310/jdg/1226090481


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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Lothar Göttsche. Hiraku Nakajima. Kōta Yoshioka. "Instanton counting and Donaldson invariants." J. Differential Geom. 80 (3) 343 - 390, November 2008.


Published: November 2008
First available in Project Euclid: 7 November 2008

zbMATH: 1172.57015
MathSciNet: MR2472477
Digital Object Identifier: 10.4310/jdg/1226090481

Rights: Copyright © 2008 Lehigh University


Vol.80 • No. 3 • November 2008
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