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Instanton counting and Donaldson invariants

2008; Lehigh University; Volume: 80; Issue: 3 Linguagem: Inglês

10.4310/jdg/1226090481

1945-743X

Lothar Göttsche, Hiraku Nakajima, Kōta Yoshioka,

Advanced Topology and Set Theory

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].