Higher dimensional analogon of Borcea-Voisin Calabi-Yau manifolds, their Hodge numbers and $L$-functions

TL;DR

This paper constructs higher-dimensional Calabi-Yau manifolds generalizing Borcea-Voisin threefolds, computes their Hodge numbers and L-functions, and introduces a method to calculate local zeta functions via Frobenius morphism.

Contribution

It provides a new higher-dimensional class of Calabi-Yau manifolds and develops techniques to compute their invariants and zeta functions.

Findings

Construction of higher-dimensional Calabi-Yau examples

Explicit computation of Hodge numbers using orbifold cohomology

Method for calculating local zeta functions with Frobenius morphism

Abstract

We construct a series of examples of Calabi-Yau manifolds in an arbitrary dimension and compute the main invariants. In particular, we give higher dimensional generalization of Borcea-Voisin Calabi-Yau threefolds. We give a method to compute a local zeta function using the Frobenius morphism for orbifold cohomology introduced by Rose. We compute Hodge numbers of the constructed examples using orbifold Chen-Ruan cohomology.