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.

UDC: 513.836

MSC: Primary 14E99, 14F25; Secondary 55U10

Received: 30.03.1977

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

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