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ISSN (electronic): 1364-0380
ISSN (print): 1465-3060
The Eynard–Orantin recursion and equivariant mirror symmetry for the projective line

Bohan Fang, Chiu-Chu Melissa Liu and Zhengyu Zong

Geometry & Topology 21 (2017) 2049–2092
Abstract

We study the equivariantly perturbed mirror Landau–Ginzburg model of 1. We show that the Eynard–Orantin recursion on this model encodes all-genus, all-descendants equivariant Gromov–Witten invariants of 1. The nonequivariant limit of this result is the Norbury–Scott conjecture, while by taking large radius limit we recover the Bouchard–Mariño conjecture on simple Hurwitz numbers.

Keywords
Gromov–Witten invariants, mirror symmetry, Eynard–Orantin recursion, Norbury–Scott conjecture
Mathematical Subject Classification 2010
Primary: 14N35
References
Publication
Received: 6 December 2014
Revised: 24 May 2016
Accepted: 16 July 2016
Published: 19 May 2017
Proposed: Lothar Göttsche
Seconded: Richard Thomas, Dan Abramovich
Authors
Bohan Fang
Beijing International Center for Mathematical Research
Peking University
5 Yiheyuan Road
Jingchunyuan 78
Beijing, 100871
China
Chiu-Chu Melissa Liu
Department of Mathematics
Columbia University
Room 623, Mail Code 4435
2990 Broadway
New York, NY 10027
United States
Zhengyu Zong
Yau Mathematical Sciences Center
Tsinghua University
Jing Chun Yuan West Building, Tsinghua University
Haidian District
Beijing, 100084
China