## Journal of Differential Geometry

### Instanton counting and Donaldson invariants

#### Abstract

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].

#### Article information

Source
J. Differential Geom., Volume 80, Number 3 (2008), 343-390.

Dates
First available in Project Euclid: 7 November 2008

https://projecteuclid.org/euclid.jdg/1226090481

Digital Object Identifier
doi:10.4310/jdg/1226090481

Mathematical Reviews number (MathSciNet)
MR2472477

Zentralblatt MATH identifier
1172.57015

#### Citation

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