Journal of Differential Geometry

LG/CY correspondence for elliptic orbifold curves via modularity

Yefeng Shen and Jie Zhou

Full-text: Access denied (no subscription detected)

We're sorry, but we are unable to provide you with the full text of this article because we are not able to identify you as a subscriber. If you have a personal subscription to this journal, then please login. If you are already logged in, then you may need to update your profile to register your subscription. Read more about accessing full-text

Abstract

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.

Article information

Source
J. Differential Geom., Volume 109, Number 2 (2018), 291-336.

Dates
Received: 14 April 2016
First available in Project Euclid: 23 May 2018

Permanent link to this document
https://projecteuclid.org/euclid.jdg/1527040874

Digital Object Identifier
doi:10.4310/jdg/1527040874

Mathematical Reviews number (MathSciNet)
MR3807321

Zentralblatt MATH identifier
06877021

Subjects
Primary: 11Fxx: Discontinuous groups and automorphic forms [See also 11R39, 11S37, 14Gxx, 14Kxx, 22E50, 22E55, 30F35, 32Nxx] {For relations with quadratic forms, see 11E45} 14N35: Gromov-Witten invariants, quantum cohomology, Gopakumar-Vafa invariants, Donaldson-Thomas invariants [See also 53D45]

Citation

Shen, Yefeng; Zhou, Jie. LG/CY correspondence for elliptic orbifold curves via modularity. J. Differential Geom. 109 (2018), no. 2, 291--336. doi:10.4310/jdg/1527040874. https://projecteuclid.org/euclid.jdg/1527040874


Export citation