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

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Abstract

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.

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Acknowledgments

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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Authors and Affiliations

  1. Graduate School of Informatics and Engineering, The University of Electro-Communications, 1-chome 5-1 Chofugaoka, Tokyo, Chofu-shi, 182-8585, Japan

    Masahiro Ohno

  2. Tsuru University, 3-8-1 Tahara, Yamanashi, Tsuru-shi, 402-8555, Japan

    Hiroyuki Terakawa

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  1. Masahiro Ohno
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  2. Hiroyuki Terakawa
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Correspondence to Masahiro Ohno.

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Ohno, M., Terakawa, H. A spectral sequence and nef vector bundles of the first Chern class two on hyperquadrics. Ann Univ Ferrara 60, 397–406 (2014). https://doi.org/10.1007/s11565-013-0188-6

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  • DOI: https://doi.org/10.1007/s11565-013-0188-6

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