This article is cited in 7 scientific papers (total in 7 papers)
Canonical singularities of three-dimensional hypersurfaces
D. G. Markushevich
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.
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Mathematics of the USSR-Izvestiya, 1986, 26:2, 315–345
D. G. Markushevich, “Canonical singularities of three-dimensional hypersurfaces”, Izv. Akad. Nauk SSSR Ser. Mat., 49:2 (1985), 334–368; Math. USSR-Izv., 26:2 (1986), 315–345
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\paper Canonical singularities of three-dimensional hypersurfaces
\jour Izv. Akad. Nauk SSSR Ser. Mat.
\jour Math. USSR-Izv.
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