A note on embeddings of S₄ and A₅ into the Cremona group and versal Galois coverings

2005/10/24 by Shinzo Bannai, Bannai, Shinzo, Hiro o. Tokunaga +1
Computer Science · Mathematics · #14E20 #14L30 #Algebraic Geometry (math.AG) #Algebraic Geometry and Number Theory #Commutative Algebra and Its Applications #FOS: Mathematics #Polynomial and algebraic computation

paper · pdf · doi:10.48550/arxiv.math/0510503

openalex publication_date 2005/10/24 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

In this paper we introduce two versal S₄ coverings, and show that the two are birationaly distinct, i.e. there exists no S₄ equivariant birational map between them. We also introduce two versal A₅ coverings and show that the two are birationaly distinct also. As a corollary we obtain that there are at least three non-conjugate embbedings of S₄ (resp. A₅) into Cr₂(ℂ), the Cremona group.

Citations

• p-elementary subgroups of the Cremona group

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