Calabi-Yau Threefolds Fibred by Mirror Quartic K3 Surfaces

TL;DR

This paper classifies and describes Calabi-Yau threefolds fibred by mirror quartic K3 surfaces, linking their structure to moduli space maps and analyzing their geometric properties.

Contribution

It provides a complete explicit classification of Calabi-Yau threefolds fibred by mirror quartic K3 surfaces based on moduli space mappings.

Findings

Complete classification of such Calabi-Yau threefolds

Explicit description via moduli space maps

Analysis of Hodge numbers and deformation properties

Abstract

We study threefolds fibred by mirror quartic K3 surfaces. We begin by showing that any family of such K3 surfaces is completely determined by a map from the base of the family to the moduli space of mirror quartic K3 surfaces. This is then used to give a complete explicit description of all Calabi-Yau threefolds fibred by mirror quartic K3 surfaces. We conclude by studying the properties of such Calabi-Yau threefolds, including their Hodge numbers and deformation theory.