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
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
收藏
页码:605 / 625
页数:21
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