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

TL;DR

This paper constructs higher-dimensional Calabi-Yau hypersurfaces in products of projective lines with inertia groups containing non-commutative free groups, highlighting a distinct property from classical projective space hypersurfaces.

Contribution

It introduces a new family of Calabi-Yau hypersurfaces with non-abelian inertia groups, expanding understanding of automorphism groups in higher-dimensional algebraic geometry.

Findings

Inertia groups contain non-commutative free groups

Different from Takahashi's results on projective space hypersurfaces

Constructs explicit examples in higher dimensions

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 $\mathbb{P}^{n+1}$.