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Izv. Akad. Nauk SSSR Ser. Mat., 1985, Volume 49, Issue 2, Pages 334–368 (Mi izv1358)  

This article is cited in 7 scientific papers (total in 7 papers)

Canonical singularities of three-dimensional hypersurfaces

D. G. Markushevich


Abstract: 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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English version:
Mathematics of the USSR-Izvestiya, 1986, 26:2, 315–345

Bibliographic databases:

UDC: 513.6
MSC: 14J17
Received: 12.09.1983

Citation: 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

Citation in format AMSBIB
\Bibitem{Mar85}
\by D.~G.~Markushevich
\paper Canonical singularities of three-dimensional hypersurfaces
\jour Izv. Akad. Nauk SSSR Ser. Mat.
\yr 1985
\vol 49
\issue 2
\pages 334--368
\mathnet{http://mi.mathnet.ru/izv1358}
\mathscinet{http://www.ams.org/mathscinet-getitem?mr=791307}
\zmath{https://zbmath.org/?q=an:0595.14026}
\transl
\jour Math. USSR-Izv.
\yr 1986
\vol 26
\issue 2
\pages 315--345
\crossref{https://doi.org/10.1070/IM1986v026n02ABEH001150}


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    Citing articles on Google Scholar: Russian citations, English citations
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    This publication is cited in the following articles:
    1. Kollar J., “Flips and Abundance for Algebraic Threefolds - a Summer Seminar at the University-of-Utah (Salt-Lake-City, 1991) - Preface”, Asterisque, 1992, no. 211, 1+  mathscinet  isi
    2. SHIHOKO ISHII, YURI PROKHOROV, “HYPERSURFACE EXCEPTIONAL SINGULARITIES”, Int. J. Math, 12:06 (2001), 661  crossref
    3. I. Yu. Fedorov, “Blow-Ups of Three-Dimensional Terminal Singularities: The $cA$ Case”, Math. Notes, 71:3 (2002), 400–407  mathnet  crossref  crossref  mathscinet  zmath  isi  elib
    4. I. Yu. Fedorov, “Divisorial contractions to 3-dimensional $cDV$ points”, Sb. Math., 193:7 (2002), 1091–1102  mathnet  crossref  crossref  mathscinet  zmath  isi  elib
    5. S. A. Kudryavtsev, “Classification of three-dimensional exceptional log canonical hypersurface singularities. I”, Izv. Math., 66:5 (2002), 949–1034  mathnet  crossref  crossref  mathscinet  zmath  elib
    6. I. Yu. Fedorov, “Purely Log-Terminal Blow-Ups of Index 1”, Math. Notes, 75:6 (2004), 855–863  mathnet  crossref  crossref  mathscinet  zmath  isi  elib
    7. D. A. Stepanov, “On the resolution of 3-dimensional terminal singularities”, Math. Notes, 77:1 (2005), 117–129  mathnet  crossref  crossref  mathscinet  zmath  isi  elib  elib
  • Известия Академии наук СССР. Серия математическая Izvestiya: Mathematics
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