Classification of double octic Calabi–Yau threefolds with h1,2 ≤ 1 defined by an arrangement of eight planes

Abstract

In this paper, we propose a combinatorial approach to study Calabi–Yau threefolds constructed as a resolution of singularities of a double covering of [Formula: see text] branched along an arrangement of eight planes. We use this description to give a complete classification of arrangements of eight planes in [Formula: see text] defining Calabi–Yau threefolds modulo projective transformation with [Formula: see text] and to derive their geometric properties (Kummer surface fibrations, automorphisms, special elements in families).