Picard-Fuchs operators for octic arrangements I (The case of orphans)

TL;DR

This paper investigates 25 families of Calabi-Yau threefolds derived from octic arrangements, revealing their Picard-Fuchs operators and highlighting cases without maximal unipotent monodromy, aiding in family classification.

Contribution

It introduces a new analysis of octic arrangement pencils, identifying Picard-Fuchs operators and their orders, and demonstrates their birational properties for family distinction.

Findings

25 families of Calabi-Yau threefolds analyzed

7 cases with order two Picard-Fuchs operators

18 cases with order four Picard-Fuchs operators

Abstract

We report on $25$ families of projective Calabi-Yau threefolds that do not have a point of maximal unipotent monodromy in their moduli space. The construction is based on an analysis of certain pencils of octic arrangements that were found by C. Meyer. There are seven cases where the Picard-Fuchs operator is of order two and $18$ cases where it is of order four. The birational nature of the Picard-Fuchs operator can be used effectively to distinguish between families whose members have the same Hodge numbers.