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Izv. Akad. Nauk SSSR Ser. Mat., 1978, Volume 42, Issue 6, Pages 1227–1287 (Mi izv1965)  

This article is cited in 43 scientific papers (total in 43 papers)

Holomorphic tensors and vector bundles on projective varieties

F. A. Bogomolov


Abstract: In this paper we study vector bundles on varieties of dimension greater than one. To do this, we apply the theory of equivariant model maps developed in the paper. We prove a topological criterion for the unstability of a vector bundle on a projective surface. Using this estimate and the closedness of holomorphic forms on projective varieties we prove the inequality $c_1^2\leqslant4c_2$ for the Chern classes of a surface of general type.
Bibliography: 37 titles.

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English version:
Mathematics of the USSR-Izvestiya, 1979, 13:3, 499–555

Bibliographic databases:

UDC: 513.6
MSC: Primary 14F05, 14F10, 32L05, 32L10; Secondary 55R40, 57R20, 14J99, 55R10
Received: 05.05.1976
Revised: 28.12.1977

Citation: F. A. Bogomolov, “Holomorphic tensors and vector bundles on projective varieties”, Izv. Akad. Nauk SSSR Ser. Mat., 42:6 (1978), 1227–1287; Math. USSR-Izv., 13:3 (1979), 499–555

Citation in format AMSBIB
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\by F.~A.~Bogomolov
\paper Holomorphic tensors and vector bundles on projective varieties
\jour Izv. Akad. Nauk SSSR Ser. Mat.
\yr 1978
\vol 42
\issue 6
\pages 1227--1287
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\mathscinet{http://www.ams.org/mathscinet-getitem?mr=522939}
\zmath{https://zbmath.org/?q=an:0439.14002}
\transl
\jour Math. USSR-Izv.
\yr 1979
\vol 13
\issue 3
\pages 499--555
\crossref{https://doi.org/10.1070/IM1979v013n03ABEH002076}
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  • Известия Академии наук СССР. Серия математическая Izvestiya: Mathematics
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