Local Calabi-Yau manifolds of type (A)over-tilde via SYZ mirror symmetry

被引：17

作者：

Kanazawa, Atsushi ^{[1
]}

Lau, Siu-Cheong ^{[2
]}

机构：

[1] Kyoto Univ, Dept Math, Sakyo Ku, Kyoto 6068502, Japan

[2] Boston Univ, Dept Math & Stat, 111 Cummington Mall, Boston, MA 02215 USA

来源：

JOURNAL OF GEOMETRY AND PHYSICS | 2019年 / 139卷

关键词：

Calabi-Yau manifolds; SYZ mirror symmetry; Riemann theta functions; Toric geometry; open Gromov-Witten invariants; Abelian varieties; ABELIAN-VARIETIES; GEOMETRY; INVARIANTS; FIBRATIONS; SURFACES; CURVES; MAPS;

D O I：

10.1016/j.geomphys.2018.12.015

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

We carry out the SYZ program for the local Calabi-Yau manifolds of type (A) over tilde by developing an equivariant SYZ theory for the toric Calabi-Yau manifolds of infinite-type. Mirror geometry is shown to be expressed in terms of the Riemann theta functions and generating functions of open Gromov-Witten invariants, whose modular properties are found and studied in this article. Our work also provides a mathematical justification for a mirror symmetry assertion of the physicists Hollowood-lqbal-Vafa (Hollowood et al., 2008). (C) 2018 Elsevier B.V. All rights reserved.

引用

页码：103 / 138

页数：36

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