, Volume 60, Issue 2, pp 397–406 | Cite as

A spectral sequence and nef vector bundles of the first Chern class two on hyperquadrics

  • Masahiro OhnoEmail author
  • Hiroyuki Terakawa


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.


Nef 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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Copyright information

© Università degli Studi di Ferrara 2013

Authors and Affiliations

  1. 1.Graduate School of Informatics and EngineeringThe University of Electro-CommunicationsTokyoJapan
  2. 2.Tsuru UniversityYamanashiJapan

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