On the classification of complex vector bundles of stable rank

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On the classification of complex vector bundles of stable rank

Abstract. One describes, using a detailed analysis of Atiyah–Hirzebruch spectral sequence, the tuples of cohomology classes on a compact, complex manifold, corresponding to the Chern classes of a complex vector bundle of stable rank. This classification becomes more effective on generalized flag manifolds, where the Lie algebra formalism and concrete integrability conditions describe in constru...

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Restriction of stable rank two vector bundles

Let X be a smooth variety deened over an algebraically closed eld of arbitrary characteristic and O X (H) be a very ample line bundle on X. We show that for a semistable X-bundle E of rank two, there exists an integer m depending only on (E):H dim(X)?2 and H dim(X) such that the restriction of E to a general divisor in jmHj is again semistable. As corollaries we obtain boundedness results, and ...

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Restriction of stable rank two vector bundles in arbitrary characteristic

Let X be a smooth variety de ned over an algebraically closed eld of arbitrary characteristic and OX H be a very ample line bundle on X We show that for a semistable X bundle E of rank two there exists an integer m depending only on E H X and H X such that the restric tion of E to a general divisor in jmH j is again semistable As corollaries we obtain boundedness results and weak versions of Bo...

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ژورنال

عنوان ژورنال: Proceedings of the Indian Academy of Sciences - Section A

سال: 2006

ISSN: 0370-0089

DOI: 10.1007/bf02829745