Gromov-Witten invariants of local P2 andmodular forms

We construct a sheaf of Fock spaces over the moduli space of elliptic curves E-y with Gamma(1)(3)-level structure, arising from geometric quantization of H-1(E-y), and a global section of this Fock sheaf. The global section coincides, near appropriate limit points, with the Gromov-Witten potentials of local P-2 and of the orbifold [C-3/mu(3)]. This proves that the Gromov-Witten potentials of local P-2 are quasimodular functions for the group Gamma(1)(3), as predicted by Aganagic, Bouchard, and Klemm, and it proves the crepant resolution conjecture for [C-3/mu(3)] in all genera.