Simple finite subgroups of the Cremona group of rank 3 (Q2894545)

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scientific article; zbMATH DE number 6051371
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Simple finite subgroups of the Cremona group of rank 3
scientific article; zbMATH DE number 6051371

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    Simple finite subgroups of the Cremona group of rank 3 (English)
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    29 June 2012
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    Cremona group
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    birational automorphism
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    simple finite group
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    The following theorem is the main result of this paper: Every non-abelian simple finite subgroup of the Cremona group of rank \(3\) over \(\mathbb C\) is isomorphic to one of the groups \({\mathfrak A}_5\), \({\mathfrak A}_6\), \({\mathfrak A}_7\), \(\text{PSL}_2(7)\), \(\text{SL}_2(8)\), \(\text{PSp}_4(3)\), and all the possibilities occur. Moreover, the author classifies up to isomorphism all simple finite subgroups in the group of birational automorphisms of any rationally connected threefold over \({\mathbb C}\) and in many cases determines all birational models of the action.
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