Orphan Calabi-Yau threefold with arithmetic monodromy group

2022/10/05 by Tymoteusz Chmiel, Chmiel, Tymoteusz
Mathematics · #Advanced Algebra and Geometry #Geometric and Algebraic Topology #Finite Group Theory Research

paper · pdf · doi:10.48550/arxiv.2210.02367

Abstract

We study monodromy groups of Picard-Fuchs operators of one-parameter families of Calabi-Yau threefolds without a point of Maximal Unipotent Monodromy (orphan operators). We construct rational symplectic bases for the monodromy action for all orphan double octic Picard-Fuchs operators of order 4. As a consequence we show that monodromy groups of all double octic orphan operators are dense in Sp(4,ℤ) and identify maximally unipotent elements in all of them, except one. Finally, we prove that the monodromy group of one of these orphan operators is arithmetic.

Related

• Picard-Fuchs operators for octic arrangements I (The case of orphans)
• Monodromy of Picard-Fuchs differential equations for Calabi-Yau threefolds
• Algebraic characterization of differential operators of Calabi-Yau type
• Coefficients of the monodromy matrices of one-parameter families of double octic Calabi-Yau threefolds at a half-conifold point
• New families of Calabi-Yau 3-folds without maximal unipotent monodromy