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A spectral sequence and nef vector bundles of the first Chern class two on hyperquadrics. (English) Zbl 1408.14133
Summary: We deduce from Bondal’s theorem a spectral sequence, which yields a description, such as a resolution, of a coherent sheaf in terms of a full strong exceptional sequence. We then apply the sequence to the case of a vector bundle given with some cohomological data on a projective space; we obtain a resolution of the vector bundle in terms of exceptional line bundles, resolution which is different from that obtained by the Beilinson spectral sequence. Finally we list all known nef vector bundles of the first Chern class two on a hyperquadric of dimension greater than three.

MSC:
14J60 Vector bundles on surfaces and higher-dimensional varieties, and their moduli
14N30 Adjunction problems
14F05 Sheaves, derived categories of sheaves, etc. (MSC2010)
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