Calabi-Yau hypersurfaces in the direct product of $\mathbb{P}^{1}$ and inertia groups

Abstract

We produce the family of Calabi-Yau hypersurfaces $X_{n}$ of $(\mathbb{P}^{1})^{n+1}$ in higher dimension whose inertia group contains non commutative free groups. This is completely different from Takahashi's result \cite{ta98} for Calabi-Yau hypersurfaces $M_{n}$ of $\mathbb{P}^{n+1}$.