Gromov-Witten Invariants of Local P^2 and Modular Forms
Abstract
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 quasi-modular functions for the group Gamma_1(3), as predicted by Aganagic-Bouchard-Klemm, and proves the Crepant Resolution Conjecture for [C^3/mu_3] in all genera.
Keywords
Cite
@article{arxiv.1804.03292,
title = {Gromov-Witten Invariants of Local P^2 and Modular Forms},
author = {Tom Coates and Hiroshi Iritani},
journal= {arXiv preprint arXiv:1804.03292},
year = {2023}
}
Comments
131 pages, 9 figures; fully commented source code included as ancillary file; for video of talk, see: https://www.youtube.com/watch?v=raqkmHxCJYI and https://www.youtube.com/watch?v=sRMESF1TSOA v2: final version, to appear in Kyoto Journal of Mathematics