希尔兹布鲁赫面 Fk 的 SYZ 镜像和莫尔斯同调

IF 1.6 3区数学 Q1 MATHEMATICS

Journal of Geometry and Physics Pub Date : 2024-06-13 DOI:10.1016/j.geomphys.2024.105255

Hayato Nakanishi

引用次数: 0

摘要

我们利用镜像对的 Strominger-Yau-Zaslow 构造和 Morse 同调来研究作为复流形的 Hirzebruch 曲面 Fk 的同调镜像对称性。对于环状法诺曲面，Futaki-Kajiura 和作者在 [9]、[10]、[16] 中利用莫尔斯同调证明了同调镜像对称性。在本文中，我们将 Futaki-Kajiura 关于 Hirzebruch 曲面 F1 的结果扩展到 Fk。我们讨论了莫尔斯同调，并证明上述意义上的同调镜像对称是成立的。

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SYZ mirror of Hirzebruch surfaces Fk and Morse homotopy

We study homological mirror symmetry for Hirzebruch surfaces $F_{k}$ as complex manifolds by using the Strominger-Yau-Zaslow construction of mirror pair and Morse homotopy. For toric Fano surfaces, Futaki-Kajiura and the author proved homological mirror symmetry by using Morse homotopy in [9], [10], [16]. In this paper, we extend Futaki-Kajiura's result of the Hirzebruch surface $F_{1}$ to $F_{k}$ . We discuss Morse homotopy and show that homological mirror symmetry in the sense above holds true.

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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