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Finite 3-Subgroups in the Cremona Group of Rank 3

Authors
  • Kuznetsova, A. A.1, 2
  • 1 National Research University Higher School of Economics, Moscow, 101000, Russia , Moscow (Russia)
  • 2 École Polytechnique, Palaiseau, 91128, France , Palaiseau (France)
Type
Published Article
Journal
Mathematical Notes
Publisher
Pleiades Publishing
Publication Date
Nov 01, 2020
Volume
108
Issue
5-6
Pages
697–715
Identifiers
DOI: 10.1134/S0001434620110085
Source
Springer Nature
Keywords
License
Yellow

Abstract

Abstract We consider 3-subgroups in groups of birational automorphisms of rationally connected threefolds and show that any 3-subgroup can be generated by at most five elements. Moreover, we study groups of regular automorphisms of terminal Fano threefolds and prove that, in all cases which are not among several explicitly described exceptions any 3-subgroup of such group can be generated by at most four elements.

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