Mirror Symmetry of Calabi-Yau Manifolds Fibered by (1,8)-Polarized Abelian Surfaces

Abstract

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 ($g\leq2$) and observe nice (quasi-)modular properties in their potential functions. We also describe degenerations of Calabi-Yau manifolds over each boundary point.