Communications in Number Theory and Physics
Volume 16 (2022)
Mirror symmetry of Calabi-Yau manifolds fibered by $(1,8)$-polarized abelian surfaces
Pages: 215 – 298
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.
mirror symmetry, Gromov–Witten invariants, modular forms
2010 Mathematics Subject Classification
11G10, 14J33, 14N35
Shinobu Hosono is supported by Grant-in Aid Scientific Research C 20K03593 and A 18H03668.
Hiromichi Takagi is supported by Grant-in Aid Scientific Research C 16K05090.
Received 25 March 2021
Accepted 7 January 2022
Published 27 April 2022