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

JOURNAL OF GEOMETRY AND PHYSICS

卷:139

Article

Kanazawa, Atsushi¹  Lau, Siu-Cheong² 

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

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

关键词: Calabi-Yau manifolds;    SYZ mirror symmetry;    Riemann theta functions;    Toric geometry;    open Gromov-Witten invariants;    Abelian varieties;   

DOI  :  10.1016/j.geomphys.2018.12.015

来源: Elsevier

【 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.

【 授权许可】

Free