Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: A note on embeddings of $S_4$ and $A_5$ into the Cremona group and
  versal Galois coverings   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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The categories of this paper are: cond-mat
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The categories of this paper are: comp-gas
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The categories of this paper are: chao-dyn
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The categories of this paper are: alg-geom
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The categories of this paper are: stat
25
The categories of this paper are: patt-sol
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The categories of this paper are: hep-lat
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The categories of this paper are: supr-con
31
The categories of this paper are: ao-sci
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The categories of this paper are: atom-ph
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The categories of this paper are: quant-ph
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The categories of this paper are: chem-ph
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The categories of this paper are: mtrl-th
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The categories of this paper are: nucl-th
3
The categories of this paper are: physics
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The categories of this paper are: funct-an