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This article is cited in 12 scientific papers (total in 12 papers)
Defining relations for the Cremona group of the plane
M. Kh. Gizatullin
Abstract:
By methods of the geometry of rational surfaces and the topology of graphs and cell complexes connected with them, the author establishes defining relations, connecting projectives, and quadratic transformations, for the group of birational transformations of the plane over an algebraically closed field.
Bibliography: 11 titles.
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Mathematics of the USSR-Izvestiya, 1983, 21:2, 211–268
Bibliographic databases:
 
UDC:
513.6
MSC: Primary 14E05, 14E07; Secondary 14H35, 05C25, 05C40, 57M15
Received: 29.01.1982
Citation:
M. Kh. Gizatullin, “Defining relations for the Cremona group of the plane”, Izv. Akad. Nauk SSSR Ser. Mat., 46:5 (1982), 909–970; Math. USSR-Izv., 21:2 (1983), 211–268
Citation in format AMSBIB
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\by M.~Kh.~Gizatullin
\paper Defining relations for the Cremona group of the plane
\jour Izv. Akad. Nauk SSSR Ser. Mat.
\yr 1982
\vol 46
\issue 5
\pages 909--970
\mathnet{http://mi.mathnet.ru/izv1653}
\mathscinet{http://www.ams.org/mathscinet-getitem?mr=675525}
\zmath{https://zbmath.org/?q=an:0555.14007|0509.14011}
\transl
\jour Math. USSR-Izv.
\yr 1983
\vol 21
\issue 2
\pages 211--268
\crossref{https://doi.org/10.1070/IM1983v021n02ABEH001789}
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http://mi.mathnet.ru/eng/izv1653 http://mi.mathnet.ru/eng/izv/v46/i5/p909
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This publication is cited in the following articles:
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Yu. I. Manin, M. A. Tsfasman, “Rational varieties: algebra, geometry and arithmetic”, Russian Math. Surveys, 41:2 (1986), 51–116
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V. A. Iskovskikh, S. L. Tregub, “On birational automorphisms of rational surfaces”, Math. USSR-Izv., 38:2 (1992), 251–275
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V. A. Iskovskikh, F. K. Kabdikairov, S. L. Tregub, “Relations in the two-dimensional Cremona group over a perfect field”, Russian Acad. Sci. Izv. Math., 42:3 (1994), 427–478
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V. A. Iskovskikh, “Factorization of birational maps of rational surfaces from the viewpoint of Mori theory”, Russian Math. Surveys, 51:4 (1996), 585–652
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I. A. Cheltsov, “Birationally rigid Fano varieties”, Russian Math. Surveys, 60:5 (2005), 875–965
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A. V. Pukhlikov, “Birationally rigid varieties. I. Fano varieties”, Russian Math. Surveys, 62:5 (2007), 857–942
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Cinzia Bisi, Alberto Calabri, Massimiliano Mella, “On Plane Cremona Transformations of Fixed Degree”, J Geom Anal, 2013
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Miesener M., “On the Aut(a(2))-Action on G-Semistable Locally Free Sheaves on P-2”, Math. Nachr., 286:17-18 (2013), 1833–1849
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Yu. G. Prokhorov, “Ratsionalnye poverkhnosti”, Lekts. kursy NOTs, 24, MIAN, M., 2015, 3–76
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Cantat S., “The Cremona Group”, Algebraic Geometry: Salt Lake City 2015, Pt 1, Proceedings of Symposia in Pure Mathematics, 97, no. 1, ed. DeFernex T. Hassett B. Mustata M. Olsson M. Popa M. Thomas R., Amer Mathematical Soc, 2018, 101–142
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С. A. Shramov, “Birational automorphisms of Severi-Brauer surfaces”, Sb. Math., 211:3 (2020), 466–480
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Blanc J., Yasinsky E., “Quotients of Groups of Birational Transformations of Cubic Del Pezzo Fibrations”, J. Ecole Polytech.-Math., 7 (2020), 1089–1112
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