Geodesic
Polyhedra of algebraic varieties and dominant morphisms
Sbornik. Mathematics, Tome 35 (1979) no. 1, pp. 35-48 Cet article a éte moissonné depuis la source Math-Net.Ru

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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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     author = {V. I. Danilov},
     title = {Polyhedra of algebraic varieties and dominant morphisms},
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V. I. Danilov. Polyhedra of algebraic varieties and dominant morphisms. Sbornik. Mathematics, Tome 35 (1979) no. 1, pp. 35-48. http://geodesic.mathdoc.fr/item/SM_1979_35_1_a2/

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