Journal of Differential Geometry
- J. Differential Geom.
- Volume 80, Number 3 (2008), 343-390.
Instanton counting and Donaldson invariants
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 , 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  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 .
J. Differential Geom., Volume 80, Number 3 (2008), 343-390.
First available in Project Euclid: 7 November 2008
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Göttsche, Lothar; Nakajima, Hiraku; Yoshioka, Kōta. Instanton counting and Donaldson invariants. J. Differential Geom. 80 (2008), no. 3, 343--390. doi:10.4310/jdg/1226090481. https://projecteuclid.org/euclid.jdg/1226090481