Geodesic
Stable vector bundles on projective surfaces
Sbornik. Mathematics, Tome 81 (1995) no. 2, pp. 397-419

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An effective variant of an arithmetic criterion for instability of vector bundles on a surface is considered. Namely, a lower bound is established for the degree of a destabilizing subsheaf in a vector bundle with positive discriminant. This bound, which depends on the rank and discriminant of the bundle, is used to prove that the restrictions of stable bundles on a surface to curves are stable, and to prove a number of other results. 
@article{SM_1995_81_2_a6,
     author = {F. A. Bogomolov},
     title = {Stable vector bundles on projective surfaces},
     journal = {Sbornik. Mathematics},
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     number = {2},
     year = {1995},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/SM_1995_81_2_a6/}
}
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F. A. Bogomolov. Stable vector bundles on projective surfaces. Sbornik. Mathematics, Tome 81 (1995) no. 2, pp. 397-419. http://geodesic.mathdoc.fr/item/SM_1995_81_2_a6/