Double covers of P^3 and Calabi-Yau varieties

TL;DR

This paper investigates Calabi-Yau varieties formed as smooth double covers of projective 3-space branched along specific octic surfaces, computing their Euler numbers and describing their singularity resolutions.

Contribution

It introduces a new class of Calabi-Yau varieties as double covers of P^3 and provides explicit calculations of their topological invariants and singularity resolutions.

Findings

Computed Euler numbers for all constructed examples

Described resolutions of singularities in detail

Identified conditions for smooth Calabi-Yau models

Abstract

We study a class of Calabi-Yau varieties that can be represented as a non-singular model of a double covering of $\mathbb P^3$ branched along certain octic surfaces. We compute Euler numbers of all constructed examples and describe their resolution of singularities.