Geodesic
Canonical singularities of three-dimensional hypersurfaces
Izvestiya. Mathematics , Tome 26 (1986) no. 2, pp. 315-345

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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. 
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     author = {D. G. Markushevich},
     title = {Canonical singularities of three-dimensional hypersurfaces},
     journal = {Izvestiya. Mathematics },
     pages = {315--345},
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     volume = {26},
     number = {2},
     year = {1986},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/IM2_1986_26_2_a4/}
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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/