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

2017/09/27 by Slawomir Cynk, Cynk, Slawomir, Duco van Straten +1
Mathematics · #14J32 #Algebraic Geometry (math.AG) #FOS: Mathematics #Number Theory (math.NT) #math.AG #math.NT #msc:14J32

paper · pdf · doi:10.48550/arxiv.1709.09752

arxiv created 2017/09/27 · arxiv updated 2017/09/29

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.

Cited by

• Elliptic and K3 fibrations on double octic Calabi-Yau threefolds

Related

• Orphan Calabi-Yau threefold with arithmetic monodromy group
• The Picard-Fuchs equation of a family of Calabi-Yau threefolds without maximal unipotent monodromy
• New families of Calabi-Yau 3-folds without maximal unipotent monodromy
• Calabi-Yau conifold expansions
• Examples of Calabi-Yau threefolds parametrised by Shimura varieties