Nagoya Mathematical Journal

Maximal algebraic subgroups of the Cremona group of three variables. Imprimitive algebraic subgroups of exceptional type

Hiroshi Umemura

Full-text: Open access

Article information

Source
Nagoya Math. J., Volume 87 (1982), 59-78.

Dates
First available in Project Euclid: 14 June 2005

Permanent link to this document
https://projecteuclid.org/euclid.nmj/1118786899

Mathematical Reviews number (MathSciNet)
MR0676586

Zentralblatt MATH identifier
0466.14005

Subjects
Primary: 14E07: Birational automorphisms, Cremona group and generalizations
Secondary: 14M20: Rational and unirational varieties [See also 14E08]

Citation

Umemura, Hiroshi. Maximal algebraic subgroups of the Cremona group of three variables. Imprimitive algebraic subgroups of exceptional type. Nagoya Math. J. 87 (1982), 59--78. https://projecteuclid.org/euclid.nmj/1118786899


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References

  • [1] Blichfeldt, H. F., Finite collineation groups, The university of Chicago press, Chicago1917.
  • [2] Bourbaki, N., Groupes et algebres de Lie,Chapitres 2 et 3,Hermann, Paris1972.
  • [3] Clebsch, A., Theorie derbinaren algebraischen Formen, Teubner, Leipzig 1872.
  • [4] Enriques, F. e Fano, G.,Sui gruppi di transformazioni cremoniane dello spazio, Annali di Matematica pura ed applicata, s. 2 15 (1897), 59-98.
  • [5] Fano, G.,I gruppi di Jonquieres generalizzati, Atti della. R. Ace.di Torino, 33 (1898), 221-271.
  • [6] Lie,S., Theorie der Transformations gruppen, Teubner, Leipzig1893.
  • [7] Matsumura, H.,Onalgebraic groups of birational transformations, Lincei-R.Sc. fis.mat. e nat., 34 (1963), 151-155.
  • [8] Rosenlicht, M.,Some basic theorems on algebraic groups, Amer. J. of Math., 78 (1956), 401-443.
  • [9] Serre, J.-P., Algebres de Lie semi-simples complexes, Benjamin, NewYork1966.
  • [10] Umemura, H.,Sur les sous-groupes algebriques primitifs du groupe deCremona a trois variables, Nagoya, Math., J., 79 (1980), 47-67.
  • [11] Weber, H.,Lehrbuch der Algebra, Zweiter Band, Braunschweig 1899. Department of Mathematics Faculty of Science Nagoya University Chikusa-ku, Nagoya, UJf, Japan

See also

  • See also: Hiroshi Umemura. On the maximal connected algebraic subgroups of the Cremona group. I. Nagoya Mathematical Journal vol. 88, (1982), pp. 213-246.
  • 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.