Calabi-Yau Threefolds Fibred by Kummer Surfaces Associated to Products of Elliptic Curves

TL;DR

This paper investigates Calabi-Yau threefolds fibred by Kummer surfaces linked to products of elliptic curves, providing a construction method and analyzing their geometric properties, including Hodge numbers.

Contribution

It introduces a general construction for Calabi-Yau threefolds fibred by Kummer surfaces from lattice polarized K3 surfaces and studies their geometric features.

Findings

Constructed Calabi-Yau threefolds with specific fibred structures.

Derived explicit formulas for Hodge numbers of these threefolds.

Analyzed geometric properties of the constructed threefolds.

Abstract

We study threefolds fibred by Kummer surfaces associated to products of elliptic curves, that arise as resolved quotients of threefolds fibred by certain lattice polarized K3 surfaces under a fibrewise Nikulin involution. We present a general construction for such surfaces, before specializing our results to study Calabi-Yau threefolds arising as resolved quotients of threefolds fibred by mirror quartic K3 surfaces. Finally, we give some geometric properties of the Calabi-Yau threefolds that we have constructed, including expressions for Hodge numbers.