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Mathematics of the USSR-Izvestiya, 1972, Volume 6, Issue 5, Pages 949–1008
DOI: https://doi.org/10.1070/IM1972v006n05ABEH001909
(Mi im2343)
 

This article is cited in 28 scientific papers (total in 28 papers)

Theorems on the topological equisingularity of families of algebraic varieties and families of polynomial mappings

A. N. Varchenko
References:
Abstract: In this paper we consider families of complex or real algebraic varieties. We prove that for almost all values of the parameters both the topology of the variety and its position in space will be the same. The set of singular values of the parameters is calculated constructively. In this paper we also isolate a class of families of polynomial mappings. For such families we prove the topological equivalence of almost all the mappings included in them. These results are applied to a proof of Zariski's theorem on the fundamental group of the complement to an algebraic hypersurface.
Received: 15.02.1972
Bibliographic databases:
UDC: 513.6
MSC: Primary 14A10, 14E15; Secondary 14F05
Language: English
Original paper language: Russian
Citation: A. N. Varchenko, “Theorems on the topological equisingularity of families of algebraic varieties and families of polynomial mappings”, Math. USSR-Izv., 6:5 (1972), 949–1008
Citation in format AMSBIB
\Bibitem{Var72}
\by A.~N.~Varchenko
\paper Theorems on the topological equisingularity of families of algebraic varieties and families of polynomial mappings
\jour Math. USSR-Izv.
\yr 1972
\vol 6
\issue 5
\pages 949--1008
\mathnet{http://mi.mathnet.ru//eng/im2343}
\crossref{https://doi.org/10.1070/IM1972v006n05ABEH001909}
\mathscinet{http://mathscinet.ams.org/mathscinet-getitem?mr=337956}
\zmath{https://zbmath.org/?q=an:0251.14006}
Linking options:
  • https://www.mathnet.ru/eng/im2343
  • https://doi.org/10.1070/IM1972v006n05ABEH001909
  • https://www.mathnet.ru/eng/im/v36/i5/p957
  • This publication is cited in the following 28 articles:
    Citing articles in Google Scholar: Russian citations, English citations
    Related articles in Google Scholar: Russian articles, English articles
    Известия Академии наук СССР. Серия математическая Izvestiya: Mathematics
    Statistics & downloads:
    Abstract page:468
    Russian version PDF:178
    English version PDF:12
    References:62
    First page:3
     
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