On a B-field transform of generalized complex structures over complex tori

IF 1.6 3区数学 Q1 MATHEMATICS Journal of Geometry and Physics Pub Date : 2024-10-03 DOI:10.1016/j.geomphys.2024.105336

Kazushi Kobayashi

引用次数: 0

Abstract

Let

(X^{n}, {\overset{ˇ}{X}}^{n})

be a mirror pair of an n-dimensional complex torus

X^{n}

and its mirror partner

{\overset{ˇ}{X}}^{n}

. Then, by SYZ transform, we can construct a holomorphic line bundle with an integrable connection from each pair of a Lagrangian section of

{\overset{ˇ}{X}}^{n} \to R^{n} / Z^{n}

and a unitary local system along it, and those holomorphic line bundles with integrable connections form a dg-category

D G_{X^{n}}

. In this paper, we focus on a certain B-field transform of the generalized complex structure induced from the complex structure on

X^{n}

, and interpret it as the deformation

X_{G}^{n}

X^{n}

by a flat gerbe

G

. Moreover, we construct the deformation of

D G_{X^{n}}

associated to the deformation from

X^{n}

X_{G}^{n}

, and also discuss the homological mirror symmetry between

X_{G}^{n}

and its mirror partner on the object level.

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论复数环上广义复数结构的 B 场变换

设（Xn,Xˇn）是 n 维复环 Xn 及其镜像伙伴 Xˇn 的一对镜像。然后，通过 SYZ 变换，我们可以从 Xˇn→Rn/Zn 的每一对拉格朗日截面和沿其的单元局部系统构造出一个具有可积分连接的全形线束，这些具有可积分连接的全形线束构成一个 dg 类 DGXn。在本文中，我们将重点研究由Xn上的复结构诱导出的广义复结构的某一B场变换，并将其解释为Xn由平面格叶G的变形XGn。此外，我们还构造了与从Xn到XGn的变形相关联的DGXn的变形，并讨论了XGn与其镜像伙伴在对象层面上的同调镜像对称性。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

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来源期刊

Journal of Geometry and Physics 物理-物理：数学物理

CiteScore

2.90

自引率

6.70%

发文量

205

审稿时长

64 days

期刊介绍： The Journal of Geometry and Physics is an International Journal in Mathematical Physics. The Journal stimulates the interaction between geometry and physics by publishing primary research, feature and review articles which are of common interest to practitioners in both fields. The Journal of Geometry and Physics now also accepts Letters, allowing for rapid dissemination of outstanding results in the field of geometry and physics. Letters should not exceed a maximum of five printed journal pages (or contain a maximum of 5000 words) and should contain novel, cutting edge results that are of broad interest to the mathematical physics community. Only Letters which are expected to make a significant addition to the literature in the field will be considered. The Journal covers the following areas of research: Methods of: • Algebraic and Differential Topology • Algebraic Geometry • Real and Complex Differential Geometry • Riemannian Manifolds • Symplectic Geometry • Global Analysis, Analysis on Manifolds • Geometric Theory of Differential Equations • Geometric Control Theory • Lie Groups and Lie Algebras • Supermanifolds and Supergroups • Discrete Geometry • Spinors and Twistors Applications to: • Strings and Superstrings • Noncommutative Topology and Geometry • Quantum Groups • Geometric Methods in Statistics and Probability • Geometry Approaches to Thermodynamics • Classical and Quantum Dynamical Systems • Classical and Quantum Integrable Systems • Classical and Quantum Mechanics • Classical and Quantum Field Theory • General Relativity • Quantum Information • Quantum Gravity

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