2024/06/20 by Bin Wang, Zhiwei Zheng, Wang, Bin +1
Mathematics · #14J28 #14J50 #20B25 #Advanced Algebra and Geometry #Algebraic Geometry (math.AG) #Algebraic Geometry and Number Theory #FOS: Mathematics #Finite Group Theory Research #Group Theory (math.GR)
paper · pdf · doi:10.48550/arxiv.2406.14499
openalex publication_date 2024/06/20 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
In 2009, Dolgachev-Keum showed that finite groups of tame symplectic automorphisms of K3 surfaces in positive characteristics are subgroups of the Mathieu group of degree 23. In this paper, we utilize lattice-theoretic methods to investigate symplectic actions of finite groups G on K3 surfaces in odd characteristics. For supersingular K3 surfaces with Artin invariants at least two, we develop a new machinery called p-root pairs to constrain possible symplectic finite group actions (without the assumption of tameness). The concept of p-root pair is closely related to root systems and Weyl groups. In particular, we provide alternative proof for many results by Dolgachev-Keum and give an upper bound for the exponent of p in |G|.