Enumerative meaning of mirror maps for toric Calabi-Yau manifolds

被引：21

作者：

Chan, Kwokwai ^{[1
]}

Lau, Siu-Cheong ^{[2
]}

Tseng, Hsian-Hua ^{[3
]}

机构：

[1] Chinese Univ Hong Kong, Dept Math, Shatin, Peoples R China

[2] Harvard Univ, Dept Math, Cambridge, MA 02138 USA

[3] Ohio State Univ, Dept Math, Columbus, OH 43210 USA

来源：

ADVANCES IN MATHEMATICS | 2013年 / 244卷

关键词：

Open Gromov-Witten invariants; Mirror maps; GKZ systems; Toric manifolds; Calabi-Yau; Mirror symmetry; SYMMETRY; INTEGRALS;

D O I：

10.1016/j.aim.2013.05.018

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

We prove that the inverse of a mirror map for a toric Calabi-Yau manifold of the form K-Y, where Y is a compact toric Fano manifold, can be expressed in terms of generating functions of genus 0 open Gromov-Witten invariants defined by Fukaya-Oh-Ohta-Ono (2010) [15]. Such a relation between mirror maps and disk counting invariants was first conjectured by Gross and Siebert (2011) [24, Conjecture 0.2 and Remark 5.1] as part of their program, and was later formulated in terms of Fukaya-Oh-Ohta-Ono's invariants in the toric Calabi-Yau case in Chan et al. (2012) [8, Conjecture 1.1]. (C) 2013 Elsevier Inc. All rights reserved.

引用

页码：605 / 625

页数：21

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