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June 2018 LG/CY correspondence for elliptic orbifold curves via modularity
Yefeng Shen, Jie Zhou
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J. Differential Geom. 109(2): 291-336 (June 2018). DOI: 10.4310/jdg/1527040874


We prove the Landau–Ginzburg/Calabi–Yau correspondence between the Gromov–Witten theory of each elliptic orbifold curve and its Fan–Jarvis–Ruan–Witten theory counterpart via modularity. We show that the correlation functions in these two enumerative theories are different representations of the same set of quasi-modular forms, expanded around different points on the upper-half plane. We relate these two representations by the Cayley transform.


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Yefeng Shen. Jie Zhou. "LG/CY correspondence for elliptic orbifold curves via modularity." J. Differential Geom. 109 (2) 291 - 336, June 2018.


Received: 14 April 2016; Published: June 2018
First available in Project Euclid: 23 May 2018

zbMATH: 06877021
MathSciNet: MR3807321
Digital Object Identifier: 10.4310/jdg/1527040874

Primary: 11Fxx , 14N35

Rights: Copyright © 2018 Lehigh University

Vol.109 • No. 2 • June 2018
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