Classification of double octic Calabi-Yau threefolds defined by an arrangement of eight planes II

TL;DR

This paper classifies all arrangements of eight planes in projective three-space that produce double octic Calabi-Yau threefolds, revealing new examples with unique monodromy and modularity properties.

Contribution

It provides a complete classification of 455 arrangements, analyzes their automorphisms, and constructs novel Calabi-Yau examples with rare monodromy and modularity features.

Findings

Identified 455 combinatorial types of arrangements.

Discovered two families with three maximally unipotent monodromy points.

Constructed Calabi-Yau threefolds with new modularity phenomena.

Abstract

We present a complete classification of all arrangements of eight planes in projective threespace that give rise to double octic Calabi-Yau threefolds. Building on earlier work, we determine all 455 combinatorial types and describe the projective automorphism groups associated with each arrangement. These automorphisms allow us to identify geometrically distinguished subfamilies and elements, and to construct a rich collection of elliptic and K3 fibrations arising naturally from the singularities of the arrangements. As applications, we exhibit two one-parameter families of Calabi-Yau threefolds that each possess three pairwise non-equivalent maximally unipotent monodromy points-phenomena that are rare in known examples. We further construct two Calabi-Yau threefolds whose third cohomology decomposes, via complex multiplication, into complementary two-dimensional Hodge structures of types (1,0,1,0) and (0,1,0,1). This decomposition yields new instances of modularity not previously observed in the Calabi-Yau setting.