Inventiones mathematicae

, Volume 55, Issue 2, pp 141–163

Desingularizations of varieties of nullforms

  • Wim H. Hesselink


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  1. 1.
    Altman, A., Kleiman, S.: Introduction to Grothendieck duality theory. Lecture notes in math. 146. Berlin: Springer Verlag 1970Google Scholar
  2. 2.
    Bala, P., Carter, R.W.: Classes of unipotent elements in simple algebraic groups. Math. Proc. Camb. Phil. Soc.79, 401–425 (1976) and80, 1–18 (1976)Google Scholar
  3. 3.
    Borel, A.: Linear algebraic groups. New York: Benjamin 1969Google Scholar
  4. 4.
    Borho, W., Kraft, H.: Über Bahnen und deren Deformationen bei linearen Aktionen reduktiver Gruppen. Comment. Math. Helvetici54, 61–104 (1979)Google Scholar
  5. 5.
    Bourbaki, N.: Groupes et algèbres de Lie, chapitres 7 et 8. Paris: Hermann 1975Google Scholar
  6. 6.
    Brieskorn, E.: Singular elements of semisimple algebraic groups. Actes du Congrès International des Mathématiciens, tome II p. 279–284, 1970Google Scholar
  7. 7.
    Buchsbaum, D.A., Eisenbud, D.: Generic free resolutions and a family of generically perfect ideals. Advances in Math.18, 245–301 (1975)Google Scholar
  8. 8.
    Chevalley, C.C.: The algebraic theory of spinors. New York: Columbia University Press 1954Google Scholar
  9. 9.
    Chevalley, C.C.: Séminaire sur la classification des groupes de Lie algébriques (mimeographed notes) Paris 1956–1958Google Scholar
  10. 10.
    Concini, C. de, Procesi, C.: A characteristic free approach to invariant theory. Advances in Math.21, 330–354 (1976)Google Scholar
  11. 11.
    Demazure, M.: Désingularisation des variétés de Schubert généralisées. Ann. scient. Ec. Norm. Sup. 4e série, t.7, 53–88 (1974)Google Scholar
  12. 12.
    Dieudonné, J., Carroll, J.B.: Invariant theory old and new. Advances in Math.4, 1–80 (1970)Google Scholar
  13. 13.
    Dynkin, E.B.: Semisimple subalgebras of semisimple Lie algebras. Am. Math. Soc. Transl. Ser. 2,6, 111–245 (1957). (Mat. Sbornik N.S.30, 349–462 (1952)Google Scholar
  14. 14.
    Gerstenhaber, M.: On dominance and varieties of commuting matrices. Ann. of Math.73, 324–348 (1961)Google Scholar
  15. 15.
    Gerstenhaber, M.: Dominance over the classical groups. Ann. of Math.74, 532–569 (1961)Google Scholar
  16. 16.
    Grothendieck, A., Dieudonné, J.A.: Eléments de géometrie algébrique I. Berlin: Springer Verlag 1971Google Scholar
  17. 17.
    Grothendieck, A., Dieudonné, J.A.: Eléments de géometrie algébrique IV. Publ. Math. I.H.E.S.28 (1966),32 (1967)Google Scholar
  18. 18.
    Hesselink, W.H.: Singularities in the nilpotent scheme of a classical group. Trans. A.M.S.222, 1–32 (1976)Google Scholar
  19. 19.
    Hesselink, W.H.: Cohomology and the resolution of the nilpotent variety. Math. Ann.223, 249–252 (1976)Google Scholar
  20. 20.
    Hesselink, W.H.: Uniform instability in reductive groups. J. reine u. angewandte Math.303/304, 74–96 (1978)Google Scholar
  21. 21.
    Hesselink, W.H.: The normality of closures of orbits in a Lie algebra. Comment. Math. Helvetici54, 105–110 (1979)Google Scholar
  22. 22.
    Hesselink, W.H.: Nilpotency in classical groups over a field of characteristic 2. Math. Zeitschrift166, 165–181 (1979)Google Scholar
  23. 23.
    Hilbert, D.: Über die vollen Invariantensysteme. Math. Ann.42, 313–373 (1893) (Gesammelte Abh., Band II, Berlin: Springer Verlag 1970)Google Scholar
  24. 24.
    Kempf, G.R.: On the collapsing of homogeneous bundles. Inventiones math.37, 229–239 (1976)Google Scholar
  25. 25.
    Kempf, G.R.: Instability in invariant theory. Ann. of Math.108, 299–316 (1978)Google Scholar
  26. 26.
    Kostant, B.: Lie group representations in polynomial rings. Amer. J. Math.85, 327–404 (1963)Google Scholar
  27. 27.
    Kraft, H., Procesi, C.: Closures of conjugacy classes of matrices are normal. Preprint, Bonn, 1978Google Scholar
  28. 28.
    Luna, D.: Slices étales. Bull. Soc. math. France, Mém.33, 81–105 (1973)Google Scholar
  29. 29.
    Lusztig, G.: On the finiteness of the number of unipotent classes. Inventiones math.34, 201–213 (1976)Google Scholar
  30. 30.
    Mumford, D.: Geometric Invariant Theory. Ergebnisse Band 34. Berlin: Springer Verlag 1965Google Scholar
  31. 31.
    Richardson, R.W.: Conjugacy classes in Lie algebras and algebraic groups. Ann. of Math.86, 1–15 (1967)Google Scholar
  32. 32.
    Rousseau, G.: Immeubles sphériques et theorie des invariants. C.R. Acad. Sc. Paris286, A247–250 (1978)Google Scholar
  33. 33.
    Schwartz, G.W.: Representations of simple Lie groups with a free module of covariants. Inventiones math.50, 1–12 (1978)Google Scholar
  34. 34.
    Slodowy, P.: Einfache Singularitäten und einfache algebraische Gruppen. Regensburger math. Schriften 2, 1978Google Scholar
  35. 35.
    Springer, T.A.: Some arithmetical results on semi-simple Lie algebras. Publ. Math. I.H.E.S.30, 115–141 (1966)Google Scholar
  36. 36.
    Springer, T.A.: The unipotent variety of a semisimple group. In: Proceedings of the Bombay Colloquium on Algebraic Geometry, p. 373–391, 1968Google Scholar
  37. 37.
    Springer, T.A.: Invariant theory. Lecture notes in math. 585. Berlin: Springer Verlag 1977Google Scholar
  38. 38.
    Steinberg, R.: Regular elements of semisimple algebraic groups. Publ. Math. I.H.E.S.25, 49–80 (1965)Google Scholar
  39. 39.
    Steinberg, R.: Conjugacy classes in algebraic groups. Lecture notes in math. 366. Berlin: Springer Verlag 1974Google Scholar
  40. 40.
    Steinberg, R.: On the desingularization of the unipotent variety. Inventiones math.36, 209–224 (1976)Google Scholar
  41. 41.
    Veldkamp, F.D.: The center of the universal enveloping algebra of a Lie algebra in characteristic p. Ann. scient. Ec. Norm. Sup. 4e série, t.5, 217–240 (1972)Google Scholar

Copyright information

© Springer-Verlag 1979

Authors and Affiliations

  • Wim H. Hesselink
    • 1
  1. 1.Department of MathematicsGroningen UniversityGroningenThe Netherlands

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