由$(1,8)$-极化阿贝尔曲面纤维的Calabi-Yau流形的镜像对称性

IF 1.2 3区数学 Q1 MATHEMATICS

Communications in Number Theory and Physics 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

Communications in Number Theory and Physics MATHEMATICS, APPLIED-MATHEMATICS

CiteScore

2.70

自引率

5.30%

发文量

审稿时长

>12 weeks

期刊介绍： Focused on the applications of number theory in the broadest sense to theoretical physics. Offers a forum for communication among researchers in number theory and theoretical physics by publishing primarily research, review, and expository articles regarding the relationship and dynamics between the two fields.