Canonical singularities of three-dimensional hypersurfaces

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.