K3 surface entropy and automorphism groups

2022/11/14 by Yu Xun, Yu, Xun · 2 citations
Mathematics · #Advanced Differential Equations and Dynamical Systems #Algebraic Geometry (math.AG) #Algebraic Geometry and Number Theory #Commutative Algebra and Its Applications #FOS: Mathematics

paper · pdf · doi:10.48550/arxiv.2211.07526

openalex publication_date 2022/11/14 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We derive a characterization of the complex projective K3 surfaces which have automorphisms of positive entropy in term of their Néron-Severi lattices. Along the way, we classify the projective K3 surfaces of zero entropy with infinite automorphism groups and we determine the projective K3 surfaces of Picard number at least five with almost abelian automorphism groups, which gives an answer to a long standing question of Nikulin.

Cited by

• Virtually abelian symmetry groups of hyperbolic lattices
• On K3 surfaces with hyperbolic automorphism groups

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