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Bounds for Chern classes of semistable vector bundles on complex projective spaces

Wiera Dobrowolska — 1993

Colloquium Mathematicae

This work concerns bounds for Chern classes of holomorphic semistable and stable vector bundles on $ℙ^{n}$ . Non-negative polynomials in Chern classes are constructed for 4-vector bundles on $ℙ^{4}$ and a generalization of the presented method to r-bundles on $ℙ^{n}$ is given. At the end of this paper the construction of bundles from complete intersection is introduced to see how rough the estimates we obtain are.

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