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On the number of real and complex moduli of singularities of smooth functions and realizations of matroids

  • V. A. Vasil'ev
  • V. V. Serganova
Article

Keywords

Smooth Function Complex Modulo 
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Literature cited

  1. 1.
    V. I. Arnol'd, A. N. Varchenko, and S. M. Gusein-Zade, Singularities of Differentiable Mappings [in Russian], Nauka, Moscow (1982).Google Scholar
  2. 2.
    D. T. Le and C. P. Ramanujam, “The invariance of Milnor numbers implies the invariance of the topological type,” Am. J. Math.,98, 67–68 (1976).Google Scholar
  3. 3.
    A. N. Varchenko, “Complex singularity index does not change along the stratum μ=const,” Funkts. Anal. Prilozh.,16, No. 1, 1–12 (1982).Google Scholar
  4. 4.
    I. Luengo, The μ=const Stratum is not Smooth, Preprint (1985).Google Scholar
  5. 5.
    M. Aigner, Combinatorial Theory [Russian translation], Mir, Moscow (1982).Google Scholar
  6. 6.
    I. M. Gel'fand and V. V. Serganova, “Combinatorial geometries and the strata of a torus on homogeneous compact manifolds,” Usp. Mat. Nauk,42, No. 2, 107–134 (1987).Google Scholar
  7. 7.
    J. Wahl, “Equisingular deformations of plane algebraic curves,” Trans. Am. Math. Soc.,193, 143–170 (1974).Google Scholar
  8. 8.
    V. I. Arnol'd, “Some open problems in the theory of singularities,” Trudy. Sem. S. L. Soboleva, No. 1, 5–15 (1976).Google Scholar
  9. 9.
    A. M. Gabrielov, “Bifurcations, Dynkin diagrams, and modality of isolated singularities,” Funkts. Anal.,8, No. 2, 7–12 (1974).Google Scholar
  10. 10.
    S. I. Gusein-Zade, “Dynkin diagrams of the singularities of functions of two variables,” Funkts. Anal.,8, No. 4, 23–30 (1974).Google Scholar
  11. 11.
    N. A'Campo, “Le group de monodromic du déploiement des singularités isolées de courbes planes,” Math. Ann.,213, No. 1, 1–32 (1975).Google Scholar
  12. 12.
    N. E. Mnev, “Varieties of combinatorial types of protective configurations and convex polyhedra,” Dokl. Akad. Nauk SSSR,283, No. 6, 1312–1314 (1985).Google Scholar
  13. 13.
    N. A'Campo, “La fonction zeta d'une monodromie,” Commun. Math. Helv.,50, No. 2, 233–248 (1975).Google Scholar
  14. 14.
    B. Teissier, “Cycles évanescents, sections planes et conditions de Whitney,” Astersque, Nos. 7–8, 285–362 (1973).Google Scholar
  15. 15.
    A. M. Gabriélov and A. G. Kushnirenko, “Description of deformations with constant Milnor numbers for homogeneous functions,” Funkts. Anal.,9, No. 4, 67–68 (1974).Google Scholar

Copyright information

© Plenum Publishing Corporation 1991

Authors and Affiliations

  • V. A. Vasil'ev
    • 1
  • V. V. Serganova
    • 1
  1. 1.M. V. Keldysh Institute of Applied MathematicsAcademy of Sciences of the USSRUSSR

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