Quotients of the Dwork Pencil

TL;DR

This paper explores the geometric properties of the Dwork pencil across dimensions, focusing on automorphism groups and quotient spaces, and computes their Hodge numbers using orbifold cohomology techniques.

Contribution

It provides a detailed analysis of automorphism groups and quotient geometries of the Dwork pencil, including explicit Hodge number calculations for these quotients.

Findings

Automorphism group G of the generic fiber is characterized.

Quotients of the Dwork pencil by subgroups are constructed and analyzed.

Hodge numbers of the quotients are computed using orbifold cohomology.

Abstract

In this paper we investigate the geometry of the Dwork pencil in any dimension. More specifically, we study the automorphism group G of the generic fiber of the pencil over the complex projective line, and the quotients of it by various subgroups of G. In particular, we compute the Hodge numbers of these quotients via orbifold cohomology.