SO(3)-Donaldson invariants of CP^2 and Mock Theta Functions

Understand

We compute the Moore-Witten regularized u-plane integral on CP^2, and we confirm their conjecture that it is the generating function for the SO(3)-Donaldson invariants of CP^2.

• We prove this conjecture using the theory of mock theta functions and harmonic Maass forms.
• We also derive further such generating functions for the SO(3)-Donaldson invariants with 2N_f massless monopoles using the geometry of certain rational elliptic surfaces (N_f=0,2,3,4).
• We show that the partition function for N_f=4 is nearly modular.