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A Note on Cohomologies of Exceptional Bundles on a Quadric Surface

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Algebraic Geometry and its Applications

Part of the book series: Aspects of Mathematics ((ASMA,volume 25))

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Abstract

We prove that only one cohomology group could be different from zero for those exceptional vector bundles on a quadric surface which appear to be symmetric ones twisted by a line bundle, and that this is not true for ext-groups between two such bundles.

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References

  1. A.I. BONDAL, A.L. GORODENTSEV. On the Functors Ext Applied to Exceptional Bundles on ℙ2, in “Helices and Vector Bundles: Seminaire Rudakov”, Lond. Math. Soc., Lect. Notes Ser. 148(1990), p.39–44.

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  2. J.-M. DREZET. Fibrés exceptionnels et suite spectrale de Beilinson généralisée sur ℙ2(ℂ), Math. Ann., B.275, h.1, (1986), p.25–48.

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  3. J.-M. DREZET, J. LE POTIER. Fibrés stables et Fibrés exceptionnels sur ℙ2, Ann.sciet., ENS, 4 serie, t.18, (1985), p.193–243.

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  4. A.L. GORODENTSEV. Exceptional vector bundles on surfaces with moveable anticanonical divisor, Math. USSR Izv. ser. math. 1988, v.52 N4, p.740–750 (Russian).

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  5. A.L. GORODENTSEV, A.N. RUDAKOV. Exceptional vector bundles on the projective spaces, Duke Math. J. 1987, v.54, N1, p.115–130.

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  6. A.N. RUDAKOV. Exceptional vector bundles on a quadric, Math. USSR Izv., ser. math. 1988, v.52, N4, p.782–812.

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  7. A.N. RUDAKOV. Adescription of Chern classes of semistable sheaves on a quadric surface, Preprint Erlangen 1990.

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Authors
  1. Alexei N. Rudakov
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Editors and Affiliations

  1. Department of Mathematics, State Pedagogical Institute, Respublikanskayastr. 108, Yaroslavl’, 150000, Russia

    Alexander Tikhomirov

  2. Steklov Mathematical Institute, Vavilova 42, Moscow, 117966, Russia

    Andrej Tyurin

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© 1994 Friedr. Vieweg & Sohn Verlagsgesellschaft mbH, Braunschweig/Wiesbaden

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Rudakov, A.N. (1994). A Note on Cohomologies of Exceptional Bundles on a Quadric Surface. In: Tikhomirov, A., Tyurin, A. (eds) Algebraic Geometry and its Applications. Aspects of Mathematics, vol 25. Vieweg+Teubner Verlag, Wiesbaden. https://doi.org/10.1007/978-3-322-99342-7_14

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  • DOI: https://doi.org/10.1007/978-3-322-99342-7_14

  • Publisher Name: Vieweg+Teubner Verlag, Wiesbaden

  • Print ISBN: 978-3-322-99344-1

  • Online ISBN: 978-3-322-99342-7

  • eBook Packages: Springer Book Archive

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