manuscripta mathematica

, Volume 39, Issue 2–3, pp 339–357 | Cite as

Invariant subrings of ℂ[X,Y,Z] which are complete intersections

  • Kei-ichi Watanabe
  • Denis Rotillon


It is known that for every finite subgroup G of SL(2,ℂ), the invariant subring ℂ[X,Y]G is a hyper-surface. In this note we treat finite subgroups of SL(3,ℂ) and give complete classification of the finite subgroups of SL(3,ℂ) whose invariant subrings are complete intersections.


Finite Group Complete Intersection Polynomial Ring Continue Fraction Expansion Finite Subgroup 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. [1]
    H.F.Blichfeldt: Finite collineation groups, The Univ. Chicago Press, Chicago, 1917Google Scholar
  2. [1a]
    G.A.Miller, H.F.Blichfeldt and L.E.Dickson; Theory and applications of finite groups, New York: Dover Publ. Inc. 1916zbMATHGoogle Scholar
  3. [2]
    C.Chevalley: Invariants of finite groups generated by reflections, Amer. J. Math. 67, (1955)Google Scholar
  4. [3]
    A.M.Cohen: Finite complex reflection groups, Ann. Scient. E.N.S. 9, (1976)Google Scholar
  5. [4]
    V.Kac and K.Watanabe: Finite linear groups whose ring of invariants is a complete intersection, Bull. A.M.S. 6, (1982)Google Scholar
  6. [5]
    O.Riemenschneider: Deformationen von Quotientensingularitäten (nach zyklischen Gruppen), Math. Ann. 209, (1974)Google Scholar
  7. [6]
    D.Rotillon: Deux contre-exemples à une conjecture de Stanley sur les anneaux d'invariants intersections complètes, Preprint Univ. Paris-Nord (1981)Google Scholar
  8. [6a]
    D.Rotillon: Deux contre-examples à une conjecture de R.Stanley sur les anneaux d'invariants intersections complètes, C.R.A.S. 292 (9 fev. 1981)Google Scholar
  9. [7]
    R.Stanley: Relative invariants of finite groups generated by pseudo-reflections, J. of Alg. 49, (1977)Google Scholar
  10. [8]
    R.Stanley: Invariants of finite groups and thier applications to combinatorics, Bull. A.M.S. 1, (1979)Google Scholar
  11. [9]
    K.Watanabe: Certain invariant subrings are Gorenstein, I, II, Osaka J. Math. 11, (1974)Google Scholar
  12. [10]
    K.Watanabe: Invariant subrings which are complete intersections, I. (Invariant subrings of finite Abelian groups), Nagoya Math. J. 77, (1979)Google Scholar
  13. [11]
    K.Watanabe: Invariant subrings of finite groups which are complete intersections, in Commutative Algebra: Analytic Methods, (ed. by R.N.Draper), Marcel Dekker, 1982Google Scholar
  14. [12]
    T.A.Springer: Invariant Theory, Lecture Notes in Math. 585, Springer, 1977Google Scholar

Copyright information

© Springer-Verlag 1982

Authors and Affiliations

  • Kei-ichi Watanabe
    • 1
  • Denis Rotillon
    • 2
  1. 1.Department of MathematicsNagoya Institute of TechnologyNagoyaJapan
  2. 2.Department de Mathématiques Centre Scientifique et PolytechniqueUniversité Paris-NordVilletaneuseFrance

Personalised recommendations