Geodesic
Holomorphic tensors and vector bundles on projective varieties
Izvestiya. Mathematics , Tome 13 (1979) no. 3, pp. 499-555

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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. 
@article{IM2_1979_13_3_a1,
     author = {F. A. Bogomolov},
     title = {Holomorphic tensors and vector bundles on projective varieties},
     journal = {Izvestiya. Mathematics },
     pages = {499--555},
     publisher = {mathdoc},
     volume = {13},
     number = {3},
     year = {1979},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/IM2_1979_13_3_a1/}
}
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F. A. Bogomolov. Holomorphic tensors and vector bundles on projective varieties. Izvestiya. Mathematics , Tome 13 (1979) no. 3, pp. 499-555. http://geodesic.mathdoc.fr/item/IM2_1979_13_3_a1/