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

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Literature cited

  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. 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. 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. I. Luengo, The μ=const Stratum is not Smooth, Preprint (1985).

  5. M. Aigner, Combinatorial Theory [Russian translation], Mir, Moscow (1982).

    Google Scholar 

  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. J. Wahl, “Equisingular deformations of plane algebraic curves,” Trans. Am. Math. Soc.,193, 143–170 (1974).

    Google Scholar 

  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. A. M. Gabrielov, “Bifurcations, Dynkin diagrams, and modality of isolated singularities,” Funkts. Anal.,8, No. 2, 7–12 (1974).

    Google Scholar 

  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. 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. 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. N. A'Campo, “La fonction zeta d'une monodromie,” Commun. Math. Helv.,50, No. 2, 233–248 (1975).

    Google Scholar 

  14. B. Teissier, “Cycles évanescents, sections planes et conditions de Whitney,” Astersque, Nos. 7–8, 285–362 (1973).

    Google Scholar 

  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 

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Authors and Affiliations

  1. M. V. Keldysh Institute of Applied Mathematics, Academy of Sciences of the USSR, USSR

    V. A. Vasil'ev & V. V. Serganova

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  1. V. A. Vasil'ev
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  2. V. V. Serganova
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Translated from Matematicheskie Zametki, Vol. 49, No. 1, pp. 19–27, January, 1991.

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Vasil'ev, V.A., Serganova, V.V. On the number of real and complex moduli of singularities of smooth functions and realizations of matroids. Mathematical Notes of the Academy of Sciences of the USSR 49, 15–20 (1991). https://doi.org/10.1007/BF01137056

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  • DOI: https://doi.org/10.1007/BF01137056

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