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Matematicheskie Zametki, 2020, Volume 108, Issue 5, Pages 725–749
DOI: https://doi.org/10.4213/mzm12587 (Mi mzm12587) 		 
This article is cited in 3 scientific papers (total in 3 papers)

Finite 3-Subgroups in the Cremona Group of Rank 3

A. A. Kuznetsovaab

a National Research University "Higher School of Economics", Moscow
b École Polytechnique
Full-text PDF (661 kB) Citations (3)
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DOI: https://doi.org/10.4213/mzm12587
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.
Keywords: automorphism group, finite subgroup, Cremona group, rationally connected variety.
Funding agency Grant number
Russian Science Foundation 18-11-00121
This work was supported by the Russian Science Foundation under grant 18-11-00121.
Received: 24.09.2019
Revised: 12.04.2020
English version:
Mathematical Notes, 2020, Volume 108, Issue 5, Pages 697–715
DOI: https://doi.org/10.1134/S0001434620110085
Bibliographic databases:
Document Type: Article
UDC: 512
Language: Russian
Citation: A. A. Kuznetsova, “Finite 3-Subgroups in the Cremona Group of Rank 3”, Mat. Zametki, 108:5 (2020), 725–749; Math. Notes, 108:5 (2020), 697–715
Citation in format AMSBIB
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  • https://doi.org/10.4213/mzm12587
  • https://www.mathnet.ru/eng/mzm/v108/i5/p725
    • This publication is cited in the following 3 articles:
    1. K. Loginov, “A Note on 3-subgroups in the Space Cremona Group”, Commun. Algebr., 50:9 (2022), 3704–3714  crossref  mathscinet  isi  scopus
    2. Yu. G. Prokhorov, “Equivariant minimal model program”, Russian Math. Surveys, 76:3 (2021), 461–542  mathnet  crossref  crossref  mathscinet  zmath  adsnasa  isi  elib
    3. Jinsong Xu, “A remark on the rank of finitep-groups of birational automorphisms”, Comptes Rendus. Mathématique, 358:7 (2020), 827  crossref
    Citing articles in Google Scholar: Russian citations, English citations
    Related articles in Google Scholar: Russian articles, English articles
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