A spectral sequence and nef vector bundles of the first Chern class two on hyperquadrics
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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.
KeywordsNef vector bundles Hyperquadrics Spectral sequences Exceptional sequences
Mathematics Subject Classification (2000)14J60 14N30 14F05
This work was partially supported by Japan Society for the Promotion of Science Grants-in-Aid for Scientific Research Grant Number 22540043.
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