Nagoya Mathematical Journal

On the maximal connected algebraic subgroups of the Cremona group. I

Hiroshi Umemura

Full-text: Open access

Article information

Source
Nagoya Math. J., Volume 88 (1982), 213-246.

Dates
First available in Project Euclid: 14 June 2005

Permanent link to this document
https://projecteuclid.org/euclid.nmj/1118787013

Mathematical Reviews number (MathSciNet)
MR0683251

Zentralblatt MATH identifier
0476.14004

Subjects
Primary: 14E07: Birational automorphisms, Cremona group and generalizations
Secondary: 14M17: Homogeneous spaces and generalizations [See also 32M10, 53C30, 57T15] 14M20: Rational and unirational varieties [See also 14E08]

Citation

Umemura, Hiroshi. On the maximal connected algebraic subgroups of the Cremona group. I. Nagoya Math. J. 88 (1982), 213--246. https://projecteuclid.org/euclid.nmj/1118787013


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References

  • [1] Borel, A., Linear algebraic groups, Benjamin, New York 1969.
  • [2] Chevalley, C, Theorie des groupes de Lie, Hermann, Paris, 1968.
  • [3] Demazure, M., Sous-groupes algebriques de rang maximum du groupe de Cremona, Ann. Scient. Ec. Norm. Sup., 4e series, 3 (1970), 507-588.
  • [4] Enriques, F., Sui gruppi continui di transformazioni crenomiane nel piano, Rendic. Accad. dei Lincei, 1893, 468-473.
  • [5] Grothendieck, A., Le groupe de Brauer, I, II, Dix exposes sur la cohomologie des schemas, North-Holland, Amsterdam, 1968, 46-66, 67-87.
  • [6] Morosof, V. V., Sur les groupes primitifs, in Russian with French summary, Mat. Sb. N.S., 5 (47) (1939), 355-390.
  • [7] Rosenlicht, M., Some basic theorems on algebraic groups, Amer. J. of Math., 78 (1956), 401-443.
  • [8] Serre, J.-P., Groupes algebriques et corps de classes, Hermann, Paris, 1959.
  • [9] fLie algebras and Lie groups, Benjamin, New York, 1965.
  • [10] fLie algebras and Lie groups, Algebres de Lie semi-simples complexes, Benjamin, New York, 1966.
  • [11] Sumihiro, H., Equivariant completion, J. Math. Kyoto Univ., 14 (1974), 1-28.
  • [12] Umemura, H., Sur les sous-groupes algebriques primitifs du groupe de Cremona a trois variables, Nagoya Math. J., 79 (1980), 47-67.
  • [13] Umemura, Maximal algebraic subgroups of the Cremona group of three variables, Nagoya Math. J., 87 (1982), 59-78.
  • [14] Umemura, On the maximal connected algebraic subgroups of the Cremona group II, in preparation.
  • [15] Weil, A., On algebraic group of transformations, Amer. J. Math., 77 (1955), 355-391. Nagoya University

See also

  • See also: Hiroshi Umemura. Maximal algebraic subgroups of the Cremona group of three variables. Imprimitive algebraic subgroups of exceptional type. Nagoya Mathematical Journal vol. 87, (1982), pp. 59-78.
  • See also: Hiroshi Umemura. On the maximal connected algebraic subgroups of the Cremona group. II. Algebraic groups and related topics (Kyoto/Nagoya, 1983) Adv. Stud. Pure Math. vol. 6, pp. 349--436 North-Holland Amsterdam 1985.