Classification of surfaces of degree four having a~nonsimple singular point
Izvestiya. Mathematics , Tome 35 (1990) no. 3, pp. 607-627.

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The author obtains a classification, to within a rigid isotopy (i.e. an isotopy in the class of algebraic surfaces), of algebraic surfaces of degree four in Cp3 with isolated singularities which have at least one nonsimple singular point (i.e. a singular point different from Ap, Dp, E6, E7, and E8). Tables: 4. Figures: 6. Bibliography: 10 titles.
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A. I. Degtyarev. Classification of surfaces of degree four having a~nonsimple singular point. Izvestiya. Mathematics , Tome 35 (1990) no. 3, pp. 607-627. https://geodesic-test.mathdoc.fr/item/IM2_1990_35_3_a4/

[1] Arnold V. I., Varchenko A. H., Gusein-zade S. M., Osobennosti differentsiruemykh otobrazhenii, t. 1, Nauka, M., 1982 ; т. 2., Наука, М., 1984, В 2-х т. | MR

[2] Degtyarev A. I., Mnogochlen Aleksandera algebraicheskoi giperpoverkhnosti, Preprint LOMI R-11-86, LOMI, L., 1986 | MR

[3] Degtyarev A. I., Izotopicheskaya klassifikatsiya kompleksnykh ploskikh proektivnykh krivykh stepeni pyat, Preprint LOMI R-3-87, LOMI, L., 1987

[4] Bruce J. W., Wall C. T. C., “On the classification of cubic surfaces”, J. London Math. Soc., 19 (1979), 245–256 | DOI | MR | Zbl

[5] Swinnerton-Dyer, “An enumeration of ail varieties of degree $4$”, Amer. J. Math., 95 (1973), 403–418 | DOI | MR | Zbl

[6] Urabe T., “On quartic surfaces and sextic curves with singularities of type $\widetilde{E}_8$, $T_{2,3,7}$, $\widetilde{E}_12$”, Publ. Inst. Math. Sci. Kyoto Univ., 20 (1984), 1185–1245 | DOI | MR | Zbl

[7] Urabe T., “On quartic surfaces and sextic curves with certain singularities”, Proc. Japan Acad. Ser. A., 59 (1983), 434–437 | DOI | MR | Zbl

[8] Urabe T., “Classification of non-normal quartic surfaces”, Tokyo J. Math., 9 (1986), 265–295 | MR | Zbl

[9] Urabe T., “Elementary transformations of Dynkin graphs and singularities of quartic surfaces”, Invent. Math., 87 (1987), 549–572 | DOI | MR | Zbl

[10] Zariski O., Algebraic surfaces, Springer-Verlag, 1971 | MR | Zbl