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Subgroups of elliptic elements of the Cremona group

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 نشر من قبل Christian Urech
 تاريخ النشر 2018
  مجال البحث
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 تأليف Christian Urech




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The Cremona group is the group of birational transformations of the complex projective plane. In this paper we classify its subgroups that consist only of elliptic elements using elementary model theory. This yields in particular a description of the structure of torsion subgroups. As an appliction, we prove the Tits alternative for arbitrary subgroups of the Cremona group, generalizing a result of Cantat. We also describe solvable subgroups of the Cremona group and their derived length, refining results from Deserti.



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