Communications in Number Theory and Physics

Volume 5 (2011)

Number 1

Donaldson invariants of $\mathbb{C}\mathrm{P}^1 \times \mathbb{C}\mathrm{P}^1$ and mock theta functions

Pages: 203 – 229

DOI: http://dx.doi.org/10.4310/CNTP.2011.v5.n1.a5

Author

Andreas Malmendier (Department of Mathematics, Colby College, Waterville, Maine, U.S.A.)

Abstract

We compute the Moore–Witten regularized $u$-plane integral on $\mathbb{C}\mathrm{P}^1 \times \mathbb{C}\mathrm{P}^1$directly in a chamber where the elliptic unfolding technique fails to work. This allows us to determine explicitformulas for the SU(2) and SO(3)-Donaldson invariants of $\mathbb{C}\mathrm{P}^1 \times \mathbb{C}\mathrm{P}^1$ interms of mock modular forms.

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