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Index of a singular point of a vector field, the Petrovskii — Oleinik inequality, and mixed hodge structures

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Literature Cited

  1. V. I. Arnol'd, "Normal forms of functions in the neighborhood of degenerate critical points," Usp. Mat. Nauk,29, No. 2, 11–49 (1974).

    Google Scholar 

  2. V. I. Arnol'd, "Some unsolved problems of the theory of singularities. The theory of cubic formulas and the application of functional analysis to problems of mathematical physics," Tr. Sem. S. L. Soboleva, No. 1, Novosibirsk (1976).

  3. V. I. Arnol'd, "Modern development of the work of I. G. Petrovskii in the topology of real algebraic manifolds," Usp. Mat. Nauk,32, No. 3, 215–216 (1977).

    Google Scholar 

  4. M. F. Atiyah and I. M. Singer, "The index of elliptic operators. III," Usp. Mat. Nauk,26, No. 1, 127–182 (1969).

    Google Scholar 

  5. A. N. Varchenko, "The characteristic polynomial of the monodromy and the Newton diagram," Invent. Math.,37, 253–262 (1976).

    Google Scholar 

  6. A. Hurwitz, "Über Riemannsche Flächen mit gegebenen Verzweigungspunkten," Math. Ann.,39, 1–61 (1891).

    Google Scholar 

  7. S. M. Gusein-Zade, "Monodromy groups of isolated singularities of hypersurfaces," Usp. Mat. Nauk,32, No. 2, 23–65 (1977).

    Google Scholar 

  8. P. Deligne, "Poids dans la cohomologie des variétés algébriques," in: Proceedings of the International Congress of Math., Vol. I, Vancouver (1974), pp. 79–85.

  9. D. Eisenbud and H. Levine, "The topological degree of a finite C-map germ," Ann. Math.,106, No. 1, 19–38 (1977).

    Google Scholar 

  10. F. Klein, Riemannsche Flächen (lit.) Vorlesungen, Vols. I, II, Göttingen (1892, new printing 1906).

  11. A. G. Kuchnirenko, "Polyhedres de Newton et nombres de Milnor," Invent. Math.,32, No. 1, 1–32 (1976).

    Google Scholar 

  12. I. G. Petrovskii, "On the topology of real plane algebraic curves," Ann. Math.,39, 187–209 (1938).

    Google Scholar 

  13. I. G. Petrovskii and O. A. Oleinik, "On the topology of real algebraic surfaces," Izv. Akad. Nauk SSSR, Ser. Mat.,13, 389–402 (1949).

    Google Scholar 

  14. J. H. M. Steenbrink, "Intersection form for quasihomogeneous singularities," Report 75-09, Amsterdam Univ. (1975).

  15. J. H. M. Steenbrink, "Mixed Hodge structure on the vanishing cohomology," Report 76-06, Amsterdam Univ. (1976).

  16. J. H. M. Steenbrink, "Appendix to [15]," Amsterdam Univ. (1977).

  17. V. M. Kharlamov, "A generalization of Petrovskii's inequality," Funkts. Anal. Prilozhen.,8, No. 2, 50–56 (1974).

    Google Scholar 

  18. V. M. Kharlamov, "A generalization of Petrovskii's inequality. II," Funkts. Anal. Prilozhen.,9, No. 3, 93–94 (1975).

    Google Scholar 

  19. G. N. Khimshiashvili, "On the local degree of a smooth map," Soobshch. Akad. Nauk GruzSSR,85, No. 2, 309–311 (1977).

    Google Scholar 

  20. V. Klee, "A combinatorial analog of Poincaré duality theorem," Can. J. Math.,16, 517–531 (1964).

    Google Scholar 

  21. F. Ehlers, "Eine Klasse Komplexer Mannigfaltigheiten und die Auflösung einiger isolierten Singularitäten," Math. Ann.,218, 127–156 (1975).

    Google Scholar 

  22. R. P. Stanley, "The upper bound conjecture and Cohen—Macaulay rings," Stud. Appl. Math.,54, No. 2, 135–142 (1975).

    Google Scholar 

  23. G. A. Reisner, "Cohen—Macaulay quotients of polynomial rings," Ph. D. Thesis, Minn. Univ. (1974).

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Moscow State University. Translated from Funktsional'nyi Analiz i Ego Prilozheniya, Vol. 12, No. 1, pp. 1–14, January–March, 1978.

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Arnol'd, V.I. Index of a singular point of a vector field, the Petrovskii — Oleinik inequality, and mixed hodge structures. Funct Anal Its Appl 12, 1–12 (1978). https://doi.org/10.1007/BF01077558

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