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September 2021 Gromov–Witten invariants of local P2 and modular forms
Tom Coates, Hiroshi Iritani
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Kyoto J. Math. 61(3): 543-706 (September 2021). DOI: 10.1215/21562261-2021-0010

Abstract

We construct a sheaf of Fock spaces over the moduli space of elliptic curves Ey with Γ1(3)-level structure, arising from geometric quantization of H1(Ey), and a global section of this Fock sheaf. The global section coincides, near appropriate limit points, with the Gromov–Witten potentials of local P2 and of the orbifold [C3μ3]. This proves that the Gromov–Witten potentials of local P2 are quasimodular functions for the group Γ1(3), as predicted by Aganagic, Bouchard, and Klemm, and it proves the crepant resolution conjecture for [C3μ3] in all genera.

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Tom Coates. Hiroshi Iritani. "Gromov–Witten invariants of local P2 and modular forms." Kyoto J. Math. 61 (3) 543 - 706, September 2021. https://doi.org/10.1215/21562261-2021-0010

Information

Received: 2 March 2019; Revised: 25 March 2019; Accepted: 27 March 2019; Published: September 2021
First available in Project Euclid: 11 June 2021

Digital Object Identifier: 10.1215/21562261-2021-0010

Subjects:
Primary: 14N35
Secondary: 14J33, 53D45, 53D50

Rights: Copyright © 2021 by Kyoto University

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Vol.61 • No. 3 • September 2021
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