Zeta Functions of Monomial Deformations of Delsarte Hypersurfaces

Abstract

Let $X_\lambda$ and $X_\lambda'$ be monomial deformations of two Delsarte hypersurfaces in weighted projective spaces. In this paper we give a sufficient condition so that their zeta functions have a common factor. This generalises results by Doran, Kelly, Salerno, Sperber, Voight and Whitcher [arXiv:1612.09249], where they showed this for a particular monomial deformation of a Calabi-Yau invertible polynomial. It turns out that our factor can be of higher degree than the factor found in [arXiv:1612.09249].