Hypergeometric Groups and Dynamics on K3 Surfaces

2020/03/31 by Katsunori Iwasaki, Iwasaki, Katsunori, Yuta Takada +1
Mathematics · #Algebraic Geometry and Number Theory #Advanced Algebra and Geometry #Mathematical Dynamics and Fractals

paper · pdf · doi:10.48550/arxiv.2003.13943

Abstract

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.

Related

• K3 surface entropy and automorphism groups
• Equivariant Linearization and Rotation Domains on K3 Surfaces
• Automorphisms of positive entropy on some hyperKahler manifolds via derived automorphisms of K3 surfaces
• Coble's question and complex dynamics of inertia groups on surfaces
• Automorphismes d'entropie positive, le cas des surfaces rationnelles