A note on embeddings of $S_4$ and $A_5$ into the Cremona group and versal Galois coverings

Details A note on embeddings of $S_4$ and $A_5$ into the Cremona group and versal Galois coverings A note on embeddings of $S_4$ and $A_5$ into the Cremona group and versal Galois coverings

2005-10-24

arxiv.org/abs/math/0510503v2

Mathematics

Algebraic Geometry

12 pages. Corrected typos. Abstract added. References supplemented

Scientific paper

In this paper we introduce two versal $S_4$ coverings, and show that the two are birationaly distinct, i.e. there exists no $S_4$ equivariant birational map between them. We also introduce two versal $A_5$ 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 $S_4$ (resp. $A_5$) into $Cr_2(\mathbb{C})$, the Cremona group.

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