Homological mirror symmetry for weighted projective spaces and Morse homotopy

IF 1.2 3区数学 Q1 MATHEMATICS

Journal of Geometry and Physics Pub Date : 2025-07-04 DOI:10.1016/j.geomphys.2025.105584

Azuna Nishida

引用次数: 0

Abstract

Kontsevich and Soibelman discussed homological mirror symmetry by using the SYZ torus fibrations, where they introduced the weighted version of Fukaya-Oh's Morse homotopy on the base space of the dual torus fibration in the intermediate step. Futaki and Kajiura applied Kontsevich-Soibelman's approach to the case when a complex manifold X is a smooth compact toric manifold. There, they introduced the category of weighted Morse homotopy on the moment polytope of toric manifolds, and compared this category to the derived category of coherent sheaves on X instead of the Fukaya category. In this paper, we extend their setting to the case of toric orbifolds, and discuss this version of homological mirror symmetry for weighted projective spaces.

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加权射影空间的同调镜像对称与Morse同伦

Kontsevich和Soibelman通过使用SYZ环面纤维讨论了同调镜像对称，他们在中间步骤中在对偶环面纤维的基空间上引入了Fukaya-Oh的Morse同调的加权版本。Futaki和Kajiura将kontsevic - soibelman的方法应用于复流形X是光滑紧致环流形的情况。在那里，他们引入了环流形矩多面体上的加权Morse同伦范畴，并将这一范畴与X上相干束的派生范畴而不是Fukaya范畴进行了比较。在本文中，我们将它们的设置推广到环形轨道的情况，并讨论了这个版本的加权投影空间的同调镜像对称。

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