Degenerations of real algebraic varieties
Izvestiya. Mathematics , Tome 27 (1986) no. 1, pp. 115-140.

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Analogues of the Harnack–Thom and Petrovskii–Kharlamov inequalities are proved for a family of real algebraic varieties. An essential role in the formulation of these inequalities is played by the Picard–Lefschetz transformation for the complexification of the family. Bibliography: 14 titles.
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V. A. Krasnov. Degenerations of real algebraic varieties. Izvestiya. Mathematics , Tome 27 (1986) no. 1, pp. 115-140. http://geodesic.mathdoc.fr/item/IM2_1986_27_1_a6/

[1] Gudkov D. A., “Topologiya veschestvennykh proektivnykh algebraicheskikh mnogoobrazii”, Uspekhi matem. nauk, 29:4 (1974), 3–79 | MR | Zbl

[2] Viro O. Ya., “Postroenie mnogokomponentnykh veschestvennykh algebraicheskikh poverkhnostei”, Dokl. AN SSSR, 248:2 (1979), 279–282 | MR | Zbl

[3] Viro O. Ya., “Krivye stepeni 7, krivye stepeni 8 i gipoteza Regsdeil”, Dokl. AN SSSR, 254:6 (1980), 1306–1310 | MR | Zbl

[4] Kulikov V. S., Kulikov Vik. S., “O monodromii semeistv algebraicheskikh poverkhnostei”, Konstruktivnaya algebraicheskaya geometriya, Yaroslavl, 1981, 53–78

[5] Kharlamov V. M., “Obobschennoe neravenstvo Petrovskogo”, Funkts. analiz, i ego prilozheniya, 8:2 (1974), 50–58 | MR

[6] Arnold V. I., “Indeks osoboi tochki vektornogo polya, neravenstva Petrovskogo–Oleinik i smeshannye struktury Khodzha”, Funkts. analiz i ego prilozheniya, 12:1 (1978), 1–14 | MR

[7] Rokhlin V. A., “Sravneniya po modulyu 16 v shestnadtsatoi probleme Gilberta”, Funkts. analiz i ego prilozheniya, 6:4 (1972), 58–64 | MR | Zbl

[8] Krasnov V. A., “Neravenstva Garnaka–Toma dlya otobrazhenii veschestvennykh algebraicheskikh mnogoobrazii”, Izv. AN SSSR. Ser. matem., 47:2 (1983), 268–297 | MR

[9] Clemens C. H., “Degeneration of Kühler manifolds”, Duke Math. J., 44:2 (1977), 215–290 | DOI | MR | Zbl

[10] Griffiths P., Shmid W., “Recent development in Hodge Theory; a Discussions of techniques and results”, Proceedings of the International Colloquium on Discrete Subgroups of Lie Groups, Bombey, 1973, 31–150

[11] Steenbrink J., “Mixed Hodge structure on vanishing cohomology”, Real and complex singularities (Ninth Nordic Summer School/NAVF Sympos. Math., Oslo, 1976), Sijthoff and Noordhoff, Alphen aan den Rijn, 1977, 525–563 | MR

[12] Delin P., “Teorema Khodzha”, Matematika, 17:5 (1973), 3–56 | MR

[13] Shmid W., “Variation of Hodge Structures: The Singularities of the Period Mapping”, Inv. math., 22 (1973), 211–319 | DOI | MR

[14] Steenbrink J., “Limits of Hodge Structures”, Inv. math., 31 (1976), 229–257 | DOI | MR | Zbl