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

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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



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