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SOME MONODROMY GROUPS OF FINITE INDEX IN $\mathit{Sp}_{4}(\mathbb{Z})$

Part of: Surfaces and higher-dimensional varieties Discontinuous groups and automorphic forms Families, fibrations

Published online by Cambridge University Press:  30 March 2015

JÖRG HOFMANN  and
DUCO VAN STRATEN
JÖRG HOFMANN
Affiliation:
Institut für Mathematik, Johannes Gutenberg University, 55099 Mainz, Germany email hofmann_joerg@gmx.net
DUCO VAN STRATEN*
Affiliation:
Institut für Mathematik, Johannes Gutenberg University, 55099 Mainz, Germany email straten@mathematik.uni-mainz.de
*
✉straten@mathematik.uni-mainz.de
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Abstract

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We determine the index of five of the seven hypergeometric Calabi–Yau operators that have finite index in $\mathit{Sp}_{4}(\mathbb{Z})$ and in two cases give a complete description of the monodromy group. Furthermore, we find six nonhypergeometric Calabi–Yau operators with finite index in $\mathit{Sp}_{4}(\mathbb{Z})$, most notably a case where the index is one.

Keywords

monodromy groupsarithmetic groupsFuchsian differential equationsCalabi–Yau equations

MSC classification

Primary: 14D05: Structure of families (Picard-Lefschetz, monodromy, etc.)
Secondary: 11F06: Structure of modular groups and generalizations; arithmetic groups 14J32: Calabi-Yau manifolds

Information

Type
Research Article
Information
Journal of the Australian Mathematical Society , Volume 99 , Issue 1 , August 2015 , pp. 48 - 62
Copyright
© 2015 Australian Mathematical Publishing Association Inc. 

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