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Izv. Akad. Nauk SSSR Ser. Mat., 1982, Volume 46, Issue 5, Pages 909–970 (Mi izv1653)  

This article is cited in 10 scientific papers (total in 10 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.

Full text: PDF file (6109 kB)
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English version:
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
\Bibitem{Giz82}
\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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    Citing articles on Google Scholar: Russian citations, English citations
    Related articles on Google Scholar: Russian articles, English articles

    This publication is cited in the following articles:
    1. Yu. I. Manin, M. A. Tsfasman, “Rational varieties: algebra, geometry and arithmetic”, Russian Math. Surveys, 41:2 (1986), 51–116  mathnet  crossref  mathscinet  zmath  adsnasa  isi
    2. V. A. Iskovskikh, S. L. Tregub, “On birational automorphysms of rational surfaces”, Math. USSR-Izv., 38:2 (1992), 251–275  mathnet  crossref  mathscinet  zmath  adsnasa  isi
    3. 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  mathnet  crossref  mathscinet  zmath  adsnasa  isi
    4. V. A. Iskovskikh, “Factorization of birational maps of rational surfaces from the viewpoint of Mori theory”, Russian Math. Surveys, 51:4 (1996), 585–652  mathnet  crossref  crossref  mathscinet  zmath  adsnasa  isi
    5. I. A. Cheltsov, “Birationally rigid Fano varieties”, Russian Math. Surveys, 60:5 (2005), 875–965  mathnet  crossref  crossref  mathscinet  zmath  adsnasa  isi  elib  elib
    6. A. V. Pukhlikov, “Birationally rigid varieties. I. Fano varieties”, Russian Math. Surveys, 62:5 (2007), 857–942  mathnet  crossref  crossref  mathscinet  zmath  adsnasa  isi  elib  elib
    7. Cinzia Bisi, Alberto Calabri, Massimiliano Mella, “On Plane Cremona Transformations of Fixed Degree”, J Geom Anal, 2013  crossref
    8. 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  crossref  isi
    9. Yu. G. Prokhorov, “Ratsionalnye poverkhnosti”, Lekts. kursy NOTs, 24, MIAN, M., 2015, 3–76  mathnet  crossref  elib
    10. 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  crossref  isi
  • Известия Академии наук СССР. Серия математическая Izvestiya: Mathematics
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