由$(1,8)$-极化阿贝尔曲面纤维的Calabi-Yau流形的镜像对称性

IF 16.4 1区化学 Q1 CHEMISTRY, MULTIDISCIPLINARY

Accounts of Chemical Research Pub Date : 2022-04-27 DOI:10.4310/cntp.2022.v16.n2.a1

Shinobu Hosono, Hiromichi Takagi

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引用次数: 0

摘要

研究了具有零欧拉特征的$(1,8)$ -极化阿贝尔曲面纤维的一类Calabi-Yau流形的镜像对称性。通过全局描述参数空间，我们找到了所有期望边界点(LCSLs)，包括那些对应于Fourier-Mukai伙伴的边界点。在每个边界点上应用镜像对称，我们计算了Gromov-Witten不变量$(g \leq 2)$，并观察到它们的势函数具有很好的(拟)模性质。我们还描述了Calabi-Yau流形在每个边界点上的退化。

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Mirror symmetry of Calabi-Yau manifolds fibered by $(1,8)$-polarized abelian surfaces

We study mirror symmetry of a family of Calabi–Yau manifolds fibered by $(1,8)$-polarized abelian surfaces with Euler characteristic zero. By describing the parameter space globally, we find all expected boundary points (LCSLs), including those correspond to Fourier–Mukai partners. Applying mirror symmetry at each boundary point, we calculate Gromov–Witten invariants $(g \leq 2)$ and observe nice (quasi-)modular properties in their potential functions. We also describe degenerations of Calabi–Yau manifolds over each boundary point.

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来源期刊

Accounts of Chemical Research 化学-化学综合

CiteScore

31.40

自引率

1.10%

发文量

312

审稿时长

2 months

期刊介绍： Accounts of Chemical Research presents short, concise and critical articles offering easy-to-read overviews of basic research and applications in all areas of chemistry and biochemistry. These short reviews focus on research from the author’s own laboratory and are designed to teach the reader about a research project. In addition, Accounts of Chemical Research publishes commentaries that give an informed opinion on a current research problem. Special Issues online are devoted to a single topic of unusual activity and significance. Accounts of Chemical Research replaces the traditional article abstract with an article "Conspectus." These entries synopsize the research affording the reader a closer look at the content and significance of an article. Through this provision of a more detailed description of the article contents, the Conspectus enhances the article's discoverability by search engines and the exposure for the research.