Speaker
Description
When constructing Calabi-Yau manifolds of dimension three, we often encounter elliptic or K3 fibered Calabi-Yau manifolds, and mirror symmetry of elliptic or K3 fibered Calabi-Yau manifolds is a well-studied subject from a variety of different interests. In contrast to this, except for those given by the fiber products of elliptic surfaces, Calabi-Yau threefolds fibred by abelian surfaces are rather rare to encounter. In this talk, I will describe mirror symmetry of a family of Calabi-Yau manifolds $X$ fibered by (1,8)-polarized abelian surfaces found by Gross and Popescu in 2001, and studied by Pavanelli, with Hodge numbers $h^{1,1}(X)=h^{2,1}=2$. We find many boundary points (LCSLs) in a suitably compactified parameter space of the family and identify them as a Fourier-Mukai partner of $X$, a birational model of $X$, and also a free quotient of $X$. We calculate Gromov-Witten invariants ($g\leq 2$) from each LCSL point and observe that these are written in terms of quasi-modular forms. This talk is based on a work with Hiromichi Takagi that appeared in CNTP (2022).
