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Mat. Sb. (N.S.), 1972, Volume 89(131), Number 2(10), Pages 297–312 (Mi msb3233)  

This article is cited in 3 scientific papers (total in 3 papers)

The Euler characteristic of a family of algebraic varieties

I. V. Dolgachev


Abstract: In this paper we derive a formula for the $l$-adic Euler characteristic of a one-parameter family of algebraic varieties. We define an algebraic analog of the local monodromy of isolated singularities of algebraic hypersurfaces, defined in the complex case by Milnor. We discuss various conjectures connected with the definition of the conductor of a family of algebraic varieties.
Bibliography: 26 titles.

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English version:
Mathematics of the USSR-Sbornik, 1972, 18:2, 303–319

Bibliographic databases:

UDC: 513.015.7
MSC: Primary 14F20, 14D05; Secondary 13B15
Received: 12.10.1971

Citation: I. V. Dolgachev, “The Euler characteristic of a family of algebraic varieties”, Mat. Sb. (N.S.), 89(131):2(10) (1972), 297–312; Math. USSR-Sb., 18:2 (1972), 303–319

Citation in format AMSBIB
\Bibitem{Dol72}
\by I.~V.~Dolgachev
\paper The Euler characteristic of a~family of algebraic varieties
\jour Mat. Sb. (N.S.)
\yr 1972
\vol 89(131)
\issue 2(10)
\pages 297--312
\mathnet{http://mi.mathnet.ru/msb3233}
\mathscinet{http://www.ams.org/mathscinet-getitem?mr=327774}
\zmath{https://zbmath.org/?q=an:0226.14003}
\transl
\jour Math. USSR-Sb.
\yr 1972
\vol 18
\issue 2
\pages 303--319
\crossref{https://doi.org/10.1070/SM1972v018n02ABEH001773}


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    Citing articles on Google Scholar: Russian citations, English citations
    Related articles on Google Scholar: Russian articles, English articles

    This publication is cited in the following articles:
    1. A. N. Rudakov, I. R. Shafarevich, “Inseparable morphisms of algebraic surfaces”, Math. USSR-Izv., 10:6 (1976), 1205–1237  mathnet  crossref  mathscinet  zmath
    2. O. N. Vvedenskii, “On pairings in elliptic curves over global fields”, Math. USSR-Izv., 12:2 (1978), 225–246  mathnet  crossref  mathscinet  zmath
    3. A. N. Rudakov, I. R. Shafarevich, “Quasi-elliptic surfaces of type $K3$”, Russian Math. Surveys, 33:1 (1978), 215–216  mathnet  crossref  mathscinet  zmath
  • Математический сборник (новая серия) - 1964–1988 Sbornik: Mathematics (from 1967)
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