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.

中文翻译：

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由$(1,8)$-极化阿贝尔表面纤维化的 Calabi-Yau 流形的镜像对称性

我们研究了由具有欧拉特征零的 $(1,8)$ 偏振阿贝尔表面纤维化的 Calabi-Yau 流形族的镜像对称性。通过全局描述参数空间，我们找到了所有预期边界点（LCSL），包括那些对应于傅立叶-Mukai 伙伴的边界点。在每个边界点应用镜像对称，我们计算 Gromov–Witten 不变量 $(g \leq 2)$ 并在其势函数中观察良好的（准）模性质。我们还描述了每个边界点上的 Calabi-Yau 流形的退化。