Skip to main content
SpringerLink
Log in

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

  • Published:
manuscripta mathematica Aims and scope Submit manuscript

Abstract

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.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Similar content being viewed by others

References

  1. H.F.Blichfeldt: Finite collineation groups, The Univ. Chicago Press, Chicago, 1917

    Google Scholar 

  2. G.A.Miller, H.F.Blichfeldt and L.E.Dickson; Theory and applications of finite groups, New York: Dover Publ. Inc. 1916

    MATH  Google Scholar 

  3. C.Chevalley: Invariants of finite groups generated by reflections, Amer. J. Math. 67, (1955)

  4. A.M.Cohen: Finite complex reflection groups, Ann. Scient. E.N.S. 9, (1976)

  5. V.Kac and K.Watanabe: Finite linear groups whose ring of invariants is a complete intersection, Bull. A.M.S. 6, (1982)

  6. O.Riemenschneider: Deformationen von Quotientensingularitäten (nach zyklischen Gruppen), Math. Ann. 209, (1974)

  7. D.Rotillon: Deux contre-exemples à une conjecture de Stanley sur les anneaux d'invariants intersections complètes, Preprint Univ. Paris-Nord (1981)

  8. 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)

  9. R.Stanley: Relative invariants of finite groups generated by pseudo-reflections, J. of Alg. 49, (1977)

  10. R.Stanley: Invariants of finite groups and thier applications to combinatorics, Bull. A.M.S. 1, (1979)

  11. K.Watanabe: Certain invariant subrings are Gorenstein, I, II, Osaka J. Math. 11, (1974)

  12. K.Watanabe: Invariant subrings which are complete intersections, I. (Invariant subrings of finite Abelian groups), Nagoya Math. J. 77, (1979)

  13. K.Watanabe: Invariant subrings of finite groups which are complete intersections, in Commutative Algebra: Analytic Methods, (ed. by R.N.Draper), Marcel Dekker, 1982

  14. T.A.Springer: Invariant Theory, Lecture Notes in Math. 585, Springer, 1977

Download references

Author information

Authors and Affiliations

  1. Department of Mathematics, Nagoya Institute of Technology, Gokiso-Cho, Showa-Ku, 466, Nagoya, Japan

    Kei-ichi Watanabe

  2. Department de Mathématiques Centre Scientifique et Polytechnique, Université Paris-Nord, Villetaneuse, France

    Denis Rotillon

Authors
  1. Kei-ichi Watanabe
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Denis Rotillon
    View author publications

    You can also search for this author in PubMed Google Scholar

Rights and permissions

Reprints and permissions

About this article

Cite this article

Watanabe, Ki., Rotillon, D. Invariant subrings of ℂ[X,Y,Z] which are complete intersections. Manuscripta Math 39, 339–357 (1982). https://doi.org/10.1007/BF01165796

Download citation

  • Received:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/BF01165796

Keywords

Search

Navigation