Gromov-witten invariants of local P^2 and modular forms
File(s)modularity-localP2.pdf (1.21 MB)
Working paper
Author(s)
Coates, Tom
Iritani, Hiroshi
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.
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.
Date Issued
2019-06-02
Citation
2019
Publisher
arXiv
Identifier
http://arxiv.org/abs/1804.03292v2
Subjects
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
Publication Status
Published