Automorphisms of hyperkähler manifolds in the view of topological entropy

2004/07/28 by Keiji Oguiso, Oguiso, Keiji · 2 citations
Mathematics · #14J28 #14J40 #14J50 #37B40 #Algebraic Geometry (math.AG) #FOS: Mathematics #math.AG #msc:14J28 #msc:14J40 #msc:14J50 #msc:37B40

paper · pdf · doi:10.48550/arxiv.math/0407476

14 pages, important references are added. Two questions and relevant parts are moved because either they are known or solved by myself

arxiv created 2005/04/25 · arxiv updated 2009/12/01

Abstract

First we show that any group of automorphisms of null-entropy of a projective hyperkähler manifold M is almost abelian of rank at most ρ(M) - 2. We then characterize automorphisms of a K3 surface with null-entropy and those with positive entropy in algebro-geometric terms. We also give an example of a group of automorphisms which is not almost abelian in each dimension.

Cited by

• On K3 surfaces with hyperbolic automorphism groups
• Integral Zariski decompositions on smooth projective surfaces II

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