### Gromov-witten invariants of local P^2 and modular forms

File | Description | Size | Format | |
---|---|---|---|---|

modularity-localP2.pdf | Working paper | 1.23 MB | Adobe PDF | View/Open |

Title: | Gromov-witten invariants of local P^2 and modular forms |

Authors: | Coates, T Iritani, H |

Item Type: | Working Paper |

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. |

Issue Date: | 26-Jul-2019 |

URI: | http://hdl.handle.net/10044/1/71987 |

Keywords: | math.AG math.AG math-ph math.MP math.SG math.AG math.AG math-ph math.MP math.SG |

Notes: | 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 |

Appears in Collections: | Pure Mathematics Mathematics |