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Izvestiya: Mathematics, 2013, Volume 77, Issue 4, Pages 742–771
DOI: https://doi.org/10.1070/IM2013v077n04ABEH002659 (Mi im8021) 		 
This article is cited in 7 scientific papers (total in 7 papers)

Tori in the Cremona groups

V. L. Popovab

a Steklov Mathematical Institute of the Russian Academy of Sciences
b State University – Higher School of Economics
English version PDF (483 kB) Citations (7)
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DOI: https://doi.org/10.1070/IM2013v077n04ABEH002659
Abstract: We classify up to conjugacy all subgroups of certain types in the full, affine and special affine Cremona groups and prove that the normalizers of these subgroups are algebraic. As an application, we obtain new results on the linearization problem by generalizing Białynicki-Birula's results of 1966–67 to disconnected groups. We prove fusion theorems for $n$-dimensional tori in the affine and special affine Cremona groups of rank $n$, and introduce and discuss the notions of Jordan decomposition and torsion primes for the Cremona groups.
Keywords: Cremona group, affine Cremona group, algebraic torus, diagonalizable algebraic group, conjugate subgroups, fusion theorems, torsion primes.
Funding agency Grant number
Russian Foundation for Basic Research 11-01-00185-a
Ministry of Education and Science of the Russian Federation НШ-5139.2012.1
Russian Academy of Sciences - Federal Agency for Scientific Organizations
Received: 01.07.2012
Russian version:
Izvestiya Rossiiskoi Akademii Nauk. Seriya Matematicheskaya, 2013, Volume 77, Issue 4, Pages 103–134
DOI: https://doi.org/10.4213/im8021
Bibliographic databases:
Document Type: Article
UDC: 512.745.4
MSC: 14E07, 14L17, 14R10
Language: English
Original paper language: Russian
Citation: V. L. Popov, “Tori in the Cremona groups”, Izv. RAN. Ser. Mat., 77:4 (2013), 103–134; Izv. Math., 77:4 (2013), 742–771
Citation in format AMSBIB
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  • https://www.mathnet.ru/eng/im/v77/i4/p103
    • This publication is cited in the following 7 articles:
    Citing articles in Google Scholar: Russian citations, English citations
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    		Известия Российской академии наук. Серия математическая Izvestiya: Mathematics
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    Abstract page:659
    Russian version PDF:184
    English version PDF:8
    References:54
    First page:15
     
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