Geodesic
Classification of surfaces of degree four having a nonsimple singular point
Izvestiya. Mathematics, Tome 35 (1990) no. 3, pp. 607-627 
A. I. Degtyarev. Classification of surfaces of degree four having a nonsimple singular point. Izvestiya. Mathematics, Tome 35 (1990) no. 3, pp. 607-627. http://geodesic.mathdoc.fr/item/IM2_1990_35_3_a4/
@article{IM2_1990_35_3_a4,
     author = {A. I. Degtyarev},
     title = {Classification of surfaces of degree four having a~nonsimple singular point},
     journal = {Izvestiya. Mathematics},
     pages = {607--627},
     year = {1990},
     volume = {35},
     number = {3},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/IM2_1990_35_3_a4/}
}
TY  - JOUR
AU  - A. I. Degtyarev
TI  - Classification of surfaces of degree four having a nonsimple singular point
JO  - Izvestiya. Mathematics
PY  - 1990
SP  - 607
EP  - 627
VL  - 35
IS  - 3
UR  - http://geodesic.mathdoc.fr/item/IM2_1990_35_3_a4/
LA  - en
ID  - IM2_1990_35_3_a4
ER  - 
%0 Journal Article
%A A. I. Degtyarev
%T Classification of surfaces of degree four having a nonsimple singular point
%J Izvestiya. Mathematics
%D 1990
%P 607-627
%V 35
%N 3
%U http://geodesic.mathdoc.fr/item/IM2_1990_35_3_a4/
%G en
%F IM2_1990_35_3_a4

Voir la notice de l'article provenant de la source Math-Net.Ru

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 $\mathbf Cp^3$ with isolated singularities which have at least one nonsimple singular point (i.e. a singular point different from $A_p$, $D_p$, $E_6$, $E_7$, and $E_8$). Tables: 4. Figures: 6. Bibliography: 10 titles.

[1] Arnold V. I., Varchenko A. H., Gusein-zade S. M., Osobennosti differentsiruemykh otobrazhenii, t. 1, Nauka, M., 1982 ; С‚. 2., Наука, Рњ., 1984, Р’ 2-С... С‚. | 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