Geodesic
Chern classes of ample bundles
Sbornik. Mathematics, Tome 14 (1971) no. 1, pp. 85-98 Cet article a éte moissonné depuis la source Math-Net.Ru

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In the article “Ample vector bundles”, Publ. Math., No 29, R. Hartshorne has extended the notion of ample vector bundle to vector bundles of arbitrary rank and has raised the following question. Let $\mathscr E$ be an ample vector bundle over a nonsingular algebraic variety $X$ and assume that the rank of $\mathscr E$ is equal to $n$. Is it true that the $i$th Chern class $c_i(\mathscr E)$ is numerically positive for $i\leqslant n$? In this paper it is proved that in the case $\operatorname{dim}X=2$ the degree of the point-cycle $c_2(\mathscr E)$ is positive. Bibliography: 8 titles. 
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V. M. Barenbaum. Chern classes of ample bundles. Sbornik. Mathematics, Tome 14 (1971) no. 1, pp. 85-98. http://geodesic.mathdoc.fr/item/SM_1971_14_1_a4/

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