Classification of double octic Calabi-Yau threefolds

TL;DR

This paper introduces a combinatorial method to classify double octic Calabi-Yau threefolds with low Hodge number, revealing their geometric features and automorphisms.

Contribution

It provides the first complete classification of double octic Calabi-Yau threefolds with $h^{1,2}\, extless=1$ using a novel combinatorial approach.

Findings

Complete classification of double octic Calabi-Yau threefolds with $h^{1,2}\, extless=1$

Identification of geometric properties such as Kummer surface fibrations and automorphisms

Discovery of special elements in families of these threefolds

Abstract

In the present paper we propose a combinatorial approach to study the so called double octic Clabi--Yau threefolds. We use this description to give a complete classification of double octics with $h^{1,2}\le1$ and to derive their geometric properties (Kummer surface fibrations, automorphisms, special elements in families).