Geodesic
Canonical singularities of three-dimensional hypersurfaces
Izvestiya. Mathematics, Tome 26 (1986) no. 2, pp. 315-345 
D. G. Markushevich. Canonical singularities of three-dimensional hypersurfaces. Izvestiya. Mathematics, Tome 26 (1986) no. 2, pp. 315-345. http://geodesic.mathdoc.fr/item/IM2_1986_26_2_a4/
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     author = {D. G. Markushevich},
     title = {Canonical singularities of three-dimensional hypersurfaces},
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Voir la notice de l'article provenant de la source Math-Net.Ru

For hypersurface singularities $f=0$, certain rationality conditions are formulated in terms of the Newton diagram of $f$ and the initial terms of a series expansion of $f$. A classification of compound Du Val singular points of three-dimensional hypersurfaces (cDV-singularities of Reid) is given. A method is indicated for calculating normal forms of equations of those singular points. The method is based on the spectral sequence of the two-term upper Koszul complex of $f$ with the Newton filtration, which generalizes Arnol'd's spectral sequence for the reduction of functions to normal form. Examples of applications of the method are given. Bibliography: 6 titles.

[1] Reid M., “Canonical 3-folds”, Journées de Géometrie Algébrique d'Angers (Juillet 1979/Algebraic Geometry, Angers, 1979), Sijthoff and Noordhoff, Alphen aan den Rijn, 1980, 273–310 | MR

[2] Reid M., Minimal models of canonical 3-folds, Kyoto Uuiv., Kyoto, 1981

[3] Khovanskii A. G., “Mnogogranniki Nyutona i toricheskie mnogoobraziya”, Funkts. analiz i ego prilozh., 11:4 (1977), 56–64 | MR | Zbl

[4] Danilov V. I., “Geometriya toricheskikh mnogoobrazii”, UMN, 33:2(200) (1978), 85–134 | MR | Zbl

[5] Arnold V. I., Varchenko A. N., Gusein-Zade S. M., Osobennosti differentsiruemykh otobrazhenii, Nauka, M., 1982 | MR

[6] Weinstein A., Lectures on symplectic manifolds, Expository lectures from the CBMS Regional Conference held at the University of North Carolina, March 8–12, 1976; Regional Conference Series in Mathematics, No 29, American Mathematical Society, Providence, R.I., 1977 | MR | Zbl