The classification of quotient singularities which are complete intersections

  • Haruhisa Nakajima
  • Kei-ichi Watanabe
Conference paper
Part of the Lecture Notes in Mathematics book series (LNM, volume 1092)


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. [B]
    H. F. Blichfeld, Finite Collineation Groups, University of Chicago Press, Chicago, 1917.Google Scholar
  2. [B-E]
    D. Buchsbaum and D. Eisenbud, Algebra structure for finite free resolutions, and some structure theorems for ideals of codimension 3, Amer. J. Math. 99 (1977), 447–485.MathSciNetCrossRefMATHGoogle Scholar
  3. [Bo]
    J.-F. Boutot, Singularites rationelles et quotient par les groupes reductifs, preprint.Google Scholar
  4. [Ch]
    C. Chevalley, Invariants of finite groups generated by reflections, Amer. J. Math. 67 (1955), 778–782.MathSciNetCrossRefMATHGoogle Scholar
  5. [Co]
    A. M. Cohen, Finite complex reflection groups, Ann. Sci. Ecole Norm. Sup. 9 (1976), 379–436.MathSciNetMATHGoogle Scholar
  6. [G-W]
    S. Goto and K.-i. Watanabe, The embedding dimension and multiplicity of rational singularities which are complete intersections, preprint.Google Scholar
  7. [H]
    W. G. Huffman, Imprimitive linear groups generated by elements containing an eigenspace of codimension two, J. Algebra 63 (1980), 499–513.MathSciNetCrossRefMATHGoogle Scholar
  8. [H-E]
    M. Hochster and J. Eagon, Cohen-Macaulay rings, invariant theory, and generic perfection of determinantal loci, Amer. J. Math. 93 (1971), 1020–1058.MathSciNetCrossRefMATHGoogle Scholar
  9. [H-S]
    W. C. Huffman and N. J. A. Sloane, Most primitive groups have messey invariants, Advances in Math. 32 (1979), 118–127.MathSciNetCrossRefMATHGoogle Scholar
  10. [K-W]
    V. Kac and K.i. Watanabe, Finite linear groups whose ring of invariants is a complete intersection, Bull. Amer. Math. Soc. 6 (1982), 221–223.MathSciNetCrossRefMATHGoogle Scholar
  11. [L-T]
    J. Lipman and B. Teissier, Pseudo-rational local rings and a theorem of Briancon-Skoda about integral closures of ideals, Michigan Math. J. 28 (1981), 97–116.MathSciNetCrossRefMATHGoogle Scholar
  12. [Mo]
    T. Molien, Uber die Invarianten der linearen Substitutionsgruppen, Sitzungsber. Konig Preuss. Akad. Wiss. (1987), 1152–1156.Google Scholar
  13. [N1]
    H. Nakajima, Relative invariants of finite groups, J. Algebra 79 (1982), 218–234.MathSciNetCrossRefMATHGoogle Scholar
  14. [N2]
    H. Nakajima, Rings of invariants of finite groups which are hypersurfaces, J. Algebra 80 (1983), 279–294.MathSciNetCrossRefMATHGoogle Scholar
  15. [N3]
    H. Nakajima, Rings of invariants of finite groups which are hypersurfaces, II, Advances in Math., to appear.Google Scholar
  16. [N4]
    H. Nakajima, Quotient complete intersections of affine spaces by finite linear groups, preprint, 1982.Google Scholar
  17. [N5]
    H. Nakajima, Representations of simple Lie groups whose algebras of invariants are complete intersections, preprint, 1983.Google Scholar
  18. [Se]
    J.-P. Serre, Sur les modules projectifs, Sem. Dubreil-Pisot, 1960/1961.Google Scholar
  19. [SGA 2]
    A. Grothendieck, Cohomologie locale des faisceaux coherents et Theoremes de Lefschetz locaux et globaux (SGA 2), North-Holland, Amsterdam, 1968.MATHGoogle Scholar
  20. [Sp1]
    T. A. Springer, Regular elements of finite reflection groups, Invent. Math. 25 (1974), 159–198.MathSciNetCrossRefMATHGoogle Scholar
  21. [Sp2]
    T. A. Springer, Invariant Theory, Lect. Notes in Math. No. 585, Springer, Berlin, 1977.MATHGoogle Scholar
  22. [St1]
    R. Stanley, Relative invariants of finite groups generated by pseudo-reflections, J. Algebra 49 (1977), 134–148.MathSciNetCrossRefMATHGoogle Scholar
  23. [St2]
    R. Stanley, Hilbert functions of graded algebras, Advances in Math. 28 (1978), 57–83.MathSciNetCrossRefMATHGoogle Scholar
  24. [St3]
    R. Stanley, Invariants of finite groups and their applications to combinatorics, Bull. Amer. Math. Soc. 1 (1979), 475–511.MathSciNetCrossRefMATHGoogle Scholar
  25. [S-T]
    G. C. Shephard and J. A. Todd, Finite unitary reflection groups, Canad. J. Math. 6 (1954), 274–304.MathSciNetCrossRefMATHGoogle Scholar
  26. [Wa1]
    D. B. Wales, Linear groups of degree n containing an involution with two eigenvalues −1, II, J. Algebra 53 (1978), 58–67.MathSciNetCrossRefMATHGoogle Scholar
  27. [W1]
    K.-i. Watanabe, Certain invariant subrings are Gorenstein, II, Osaka J. Math. 11 (1974), 379–388.MathSciNetMATHGoogle Scholar
  28. [W2]
    K.-i. Watanabe, Invariant subrings which are complete intersections, I (Invariant subrings of finite Abelian groups), Nagoya Math. J. 77 (1980), 89–98.MathSciNetCrossRefGoogle Scholar
  29. [W-R]
    K.-i. Watanabe and D. Rotillon, Invariant subrings of ℂ[X,Y,Z] which are complete intersections, Manuscripta Math. 39 (1982), 339–357.MathSciNetCrossRefMATHGoogle Scholar

Copyright information

© Springer-Verlag 1984

Authors and Affiliations

  • Haruhisa Nakajima
    • 1
    • 2
  • Kei-ichi Watanabe
    • 1
    • 2
  1. 1.Department of MathematicsTokyo Metropolitan UniversityTokyoJapan
  2. 2.Department of MathematicsNagoya Institute of TechnologyNagoyaJapan

Personalised recommendations