On the Classification of Stable Rank-r Vector Bundles over the Projective Plane

  • Klaus Hulek
Part of the Progress in Mathematics book series (PM, volume 7)


Though quite a lot is known on the classification of stable rank-2 vector bundles over the projective plane, this is not the case for arbitrary rank. In my talk I wanted to give some results concerning the moduli of rank-r vector bundles. We shall restrict ourselves to c1 () = 0. The reason is that though most of the ideas should also work for c1 () ≠=0 the technical modifications which are necessary, are quite substantial, and so far I have not been able to bring them into a unified theory.


Exact Sequence Vector Bundle Projective Plane Chern Class Stable Bundle 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. [1]
    Barth, W. Some properties of stable rank-2 vector bundles on ℙn. Math. Ann. 226, 125–150 (1977).MathSciNetMATHCrossRefGoogle Scholar
  2. [2]
    Barth, W. Moduli of vector bundles on the projective plane, Invent, math. 42, 63–91 (1977).MathSciNetMATHCrossRefGoogle Scholar
  3. [3]
    Barth, W. Elencwajg, G. Concernant 1a cohomologie des fibres algébriques sta-bles sur’ n (ℂ). In Springer LN 683, Berlin-Heidelberg-New-York, Springer 1978.Google Scholar
  4. [4]
    Barth, W. Hulek, K. Monads and moduli of vector bundles. Manuscripta Math. 25, 323–347 (1978).MathSciNetMATHCrossRefGoogle Scholar
  5. [5]
    Beilinson, A.A. Coherent sheaves on ℙn and problems of linear algebra. Funktional’nyi Analiz. i. Ego Pri lozheniya, Vol. 12, No. 3, 68–69 (1978).MathSciNetMATHGoogle Scholar
  6. [6]
    Fulton, W. Hansen, J. A connectedness theorem for projective varieties, with applications to intersections and singularities of mappings. To appear in Math. Ann.Google Scholar
  7. [7]
    Maruyama, M. Openness of a family of torsion free sheaves. Journ. of Math, of Kyoto Univ., Vol. 16, Nr. 3, 627–637 (1976).MathSciNetMATHGoogle Scholar
  8. [8]
    Maruyama, M. Moduli of stable sheaves II. Journ. of Math, of Kyoto Univ., Vol. 18, No.3, 557–614 (1978).MathSciNetMATHGoogle Scholar
  9. [9]
    Mumford, D. Geometric Invariant Theory. Berlin-Heidelberg-New-York: Springer 1965.MATHGoogle Scholar
  10. [10]
    Le Potier, J. Fibrés stables de rang 2 surℙ2((ℂ). Math. Ann. 241, 217–256 (1979).MathSciNetMATHCrossRefGoogle Scholar
  11. [11]
    Takemoto, F. Stable vector bundles on algebraic surfaces. Nagoya Math. J. 47, 29–48 (1972).MathSciNetMATHGoogle Scholar
  12. [12]
    Wall, C.T.C. Nets of quadrics and theta-characteristics of singular curves. Phil. Transactions of the Roya Soc. of London, A 289, 229–269 (1978).Google Scholar

Copyright information

© Birkhäuser, Boston 1980

Authors and Affiliations

  • Klaus Hulek
    • 1
  1. 1.Mathematisches InstitutUniversität Erlangen-NürnbergErlangenWest-Germany

Personalised recommendations