Holomorphic tensors and vector bundles on projective varieties

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.
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