SO(3)-Donaldson invariants of CP2 and mock theta functions

We compute the Moore-Witten regularized u-plane integral on CP2, and we confirm the conjecture that it is the generating function for the SO(3)-Donaldson invariants of CP2. We also derive generating functions for the SO(3)-Donaldson invariants with 2N(f) massless monopoles using the geometry of certain rational elliptic surfaces (N-f is an element of {0, 2, 3, 4}), and we show that the partition function for N-f = 4 is nearly modular. Our results rely heavily on the theory of mock theta functions and harmonic Maass forms (for example, see Ono [40]).