Symmetry, Integrability and Geometry: Methods and Applications (SIGMA)

SIGMA 13 (2017), 087, 22 pages      arXiv:1706.01626      https://doi.org/10.3842/SIGMA.2017.087
Contribution to the Special Issue on Modular Forms and String Theory in honor of Noriko Yui

Zeta Functions of Monomial Deformations of Delsarte Hypersurfaces

Remke Kloosterman
Università degli Studi di Padova, Dipartimento di Matematica, Via Trieste 63, 35121 Padova, Italy

Received June 09, 2017, in final form November 01, 2017; Published online November 07, 2017

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].

Key words: monomial deformation of Delsarte surfaces; zeta functions.

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