Hypergeometric groups and dynamics on K3 surfaces

A hypergeometric group is a matrix group modeled on the monodromy group of a generalized hypergeometric differential equation. This article presents a fruitful interaction between the theory of hypergeometric groups and dynamics on K3 surfaces by showing that a certain class of hypergeometric groups...

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Bibliographic Details
Published inMathematische Zeitschrift Vol. 301; no. 1; pp. 835 - 891
Main Authors Iwasaki, Katsunori, Takada, Yuta
Format Journal Article
LanguageEnglish
Published Berlin/Heidelberg Springer Berlin Heidelberg 01.05.2022
Springer Nature B.V
Subjects
Automorphisms
Differential equations
Disks
Lattices (mathematics)
Mathematics
Mathematics and Statistics
Hypergeometric groups
Lehmer’s number
14J28
Siegel disks
14J50
Entropy
Salem numbers
K3 surfaces
Automorphisms
Unimodular lattices
33C80
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Summary:A hypergeometric group is a matrix group modeled on the monodromy group of a generalized hypergeometric differential equation. This article presents a fruitful interaction between the theory of hypergeometric groups and dynamics on K3 surfaces by showing that a certain class of hypergeometric groups and related lattices lead to a lot of K3 surface automorphisms of positive entropy, especially such automorphisms with Siegel disks.
ISSN:0025-5874
1432-1823
DOI:10.1007/s00209-021-02912-6