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Mat. Sb. (N.S.), 1971, Volume 85(127), Number 1(5), Pages 85–97 (Mi msb3185)  

Chern classes of ample bundles

V. M. Barenbaum


Abstract: In the article “Ample vector bundles”, Publ. Math., № 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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English version:
Mathematics of the USSR-Sbornik, 1971, 14:1, 85–98

Bibliographic databases:

UDC: 513.015.7
MSC: 14F05
Received: 06.05.1970

Citation: V. M. Barenbaum, “Chern classes of ample bundles”, Mat. Sb. (N.S.), 85(127):1(5) (1971), 85–97; Math. USSR-Sb., 14:1 (1971), 85–98

Citation in format AMSBIB
\Bibitem{Bar71}
\by V.~M.~Barenbaum
\paper Chern classes of ample bundles
\jour Mat. Sb. (N.S.)
\yr 1971
\vol 85(127)
\issue 1(5)
\pages 85--97
\mathnet{http://mi.mathnet.ru/msb3185}
\mathscinet{http://www.ams.org/mathscinet-getitem?mr=292095}
\zmath{https://zbmath.org/?q=an:0215.08303}
\transl
\jour Math. USSR-Sb.
\yr 1971
\vol 14
\issue 1
\pages 85--98
\crossref{https://doi.org/10.1070/SM1971v014n01ABEH002605}


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