The Alternating Groups and K3 Surfaces

2005/06/30 by De‐Qi Zhang, D. -Q. Zhang, Zhang, D. -Q.
Mathematics · #14J28 #14J30 #14J50 #Advanced Algebra and Geometry #Algebraic Geometry (math.AG) #Algebraic Geometry and Number Theory #FOS: Mathematics #Geometric and Algebraic Topology #math.AG #msc:14J28 #msc:14J30 #msc:14J50

paper · pdf · doi:10.48550/arxiv.math/0506610

Journal of Pure and Applied Algebra (21 pages) to appear

arxiv created 2005/06/30 · openalex publication_date 2005/06/30 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

In this note, we consider all possible extensions G of a non-trivial perfect group H acting faithfully on a K3 surface X. The pair (X, G) is proved to be uniquely determined by G if the transcendental value of G is maximum. In particular, we have G/H < Z/(2) + Z/(2), if H is the alternating group A₅ and normal in G.

Citations

• Lattices of Algebraic Cycles on Fermat Varieties in Positive Characteristics

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