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Mat. Sb. (N.S.), 1978, Volume 106(148), Number 3(7), Pages 357–371 (Mi msb2580)  

Polyhedra of algebraic varieties and dominant morphisms

V. I. Danilov


Abstract: We show that a proper surjective morphism of algebraic varieties gives rise to an epimorphism of the rational homology of the peripheral polyhedra associated to these varieties. We introduce a numerical invariant of noncomplete algebraic varieties and prove that it is monotone with respect to dominant morphisms. Our results are applied to the cancellation problem of algebraic varieties.
Bibliography: 8 titles.

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English version:
Mathematics of the USSR-Sbornik, 1979, 35:1, 35–48

Bibliographic databases:

UDC: 513.836
MSC: Primary 14E99, 14F25; Secondary 55U10
Received: 30.03.1977

Citation: V. I. Danilov, “Polyhedra of algebraic varieties and dominant morphisms”, Mat. Sb. (N.S.), 106(148):3(7) (1978), 357–371; Math. USSR-Sb., 35:1 (1979), 35–48

Citation in format AMSBIB
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\by V.~I.~Danilov
\paper Polyhedra of algebraic varieties and dominant morphisms
\jour Mat. Sb. (N.S.)
\yr 1978
\vol 106(148)
\issue 3(7)
\pages 357--371
\mathnet{http://mi.mathnet.ru/msb2580}
\mathscinet{http://www.ams.org/mathscinet-getitem?mr=505106}
\zmath{https://zbmath.org/?q=an:0418.14001|0398.14001}
\transl
\jour Math. USSR-Sb.
\yr 1979
\vol 35
\issue 1
\pages 35--48
\crossref{https://doi.org/10.1070/SM1979v035n01ABEH001448}
\isi{http://gateway.isiknowledge.com/gateway/Gateway.cgi?GWVersion=2&SrcApp=PARTNER_APP&SrcAuth=LinksAMR&DestLinkType=FullRecord&DestApp=ALL_WOS&KeyUT=A1979JB17500003}


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  • http://mi.mathnet.ru/eng/msb/v148/i3/p357

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