Index of a singular point of a vector field, the Petrovskii--Oleinik inequality, and mixed hodge structures
Funkcionalʹnyj analiz i ego priloženiâ, Tome 12 (1978) no. 1, pp. 1-14.

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V. I. Arnol'd. Index of a singular point of a vector field, the Petrovskii--Oleinik inequality, and mixed hodge structures. Funkcionalʹnyj analiz i ego priloženiâ, Tome 12 (1978) no. 1, pp. 1-14. http://geodesic.mathdoc.fr/item/FAA_1978_12_1_a0/

[1] Arnold V.I., “Normalnye formy funktsii v okrestnosti vyrozhdennykh kriticheskikh tochek”, UMN, XXIX:2 (1974), 11–49

[2] Arnold V.I., “Nekotorye nereshennye zadachi teorii osobennostei”, Teoriya kubaturnykh formul i prilozheniya funktsionalnogo analiza k zadacham matematicheskoi fiziki, Trudy seminara S. L. Soboleva, 1, Novosibirsk, 1976 | MR

[3] Arnold V.I., “Sovremennoe razvitie rabot I. G. Petrovskogo po topologii deistvitelnykh algebraicheskikh mnogoobrazii”, UMN, XXXII:3 (1977), 215–216

[4] Atya M.F., Zinger I.M., “Indeks ellipticheskikh operatorov. III”, UMN, XXIV:1 (1969), 127–182

[5] Varchenko A.N., “The characteristic polinomial of the monodromie and the Newton diagramm”, Invent. Math., 37 (1976), 253–262 | DOI | MR | Zbl

[6] Hurwitz A., “Über Riemannsche Flächen mit gegebenen Verzweigungspunkten”, Math. Ann., 39 (1891), 1–61 | DOI | MR

[7] Gusein-Zade C.M., “Gruppy monodromii izolirovannykh osobennostei giperpoverkhnostei”, UMN, XXXII:2 (1977), 23–65 | MR

[8] Deligne P., “Poids dans la cohomologie des varietes algebriques”, Intern. Congress of Math., v. I, Vancouver, 1974, 79–85 | MR

[9] Eisenbud D., Levine H., “The topological degree of a finite $C^\infty$-map germ”, Ann. Math., 106:1 (1977), 19–38 | DOI | MR

[10] Klein F., Riemannsche Flächen (lit.), Forles. I, II, Göttingen, 1892 (Nuedruck 1906) | MR

[11] Kuchnirenko A.G., “Polyhedres de Newton et nombres de Milnor”, Invent. Math., 32:1 (1976), 1–32 | DOI | MR

[12] Petrovsky I.G., “On the topology of real plane algebraic curves”, Ann. Math., 39 (1938), 187–209 | MR

[13] Petrovskii I.G., Oleinik O.A., “O topologii deistvitelnykh algebraicheskikh poverkhnostei”, Izv. AN SSSR, seriya matem., 13 (1949), 389–402 | MR

[14] Steenbrink J.H.M., Intersection form for quasi homogenous singularities, Report 75-09, University of Amsterdam, 1975 | MR

[15] Steenbrink J.H.M., MixedHodge structure on the vanischingcohomology, Report 76-06, University of Amsterdam, 1976 | MR

[16] Steenbrink J.H.M., Appendix to [15], University of Amsterdam, 1977

[17] Kharlamov V.M., “Obobschennoe neravenstvo Petrovskogo”, Funkts. analiz, 8:2 (1974), 50–56 | MR | Zbl

[18] Kharlamov V.M., “Obobschennoe neravenstvo Petrovskogo. II”, Funkts. analiz, 9:3 (1975), 93–94 | MR | Zbl

[19] Khimshiashvili G.N., “O lokalnoi stepeni gladkogo otobrazheniya”, Soobscheniya AN Gruz.SSR, 85:2 (1977), 309–311 | MR

[20] Klee V., “A combinatorial analog of Poincaré duality theorem”, Canad. J. Math., 16 (1964), 517–531 | DOI | MR | Zbl

[21] Ehlers F., “Eine Klasse Komplexer Mannigfaltigkeiten und die Auflösung einiger isolated Singularitäten”, Math. Ann., 218 (1975), 127–156 | DOI | MR | Zbl

[22] Stanley R.P., “The upper bound conjecture and Cohen-Macaulay rings”, Studies in Appl. Math., 54:2 (1975), 135–142 | DOI | MR | Zbl

[23] Reisner G.A., Cohen–Macaulay quotiens of polynomial rings, Ph.D. Thesis, Univ. of Minn., 1974 | MR