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Mathematische Annalen

, Volume 298, Issue 1, pp 67–78 | Cite as

Complete curves in moduli spaces of stable bundles on surfaces

  • D. Huybrechts
Article

Mathematics Subject Classification (1991)

14D20 14J60 

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References

  1. [Ba]
    Barth, W.: Moduli of vector bundles on the projective plane. Invent. Math.42, 63–91 (1977)CrossRefGoogle Scholar
  2. [BPV]
    Barth, W., Peters, C., Van de Ven, A.: Compact complex surfaces. (Ergeb. Math. Grenzgeb. 3. Folge vol. 2) Berlin Heidelberg New York: Springer 1984Google Scholar
  3. [B]
    Bogomolov, F.A.: On stability of vector bundles on surfaces and curves. Preprint (1991)Google Scholar
  4. [D]
    Donaldson S.K.: Polynomial invariants for smooth four manifolds. Topology29, 257–315 (1990)Google Scholar
  5. [D, N]
    Drezet, J.-M., Narasimhan, M.S.: Groupe de Picard des variétés de modules de fibrés semi-stables sur les courbes algébriques. Invent. Math.97, 53–94 (1989)Google Scholar
  6. [Fl]
    Flenner, H.: Restrictions of semistable bundles on projective varieties. Comment. Math. Helv.59, 635–650 (1984)Google Scholar
  7. [Gi]
    Gieseker, D.: On the moduli of vector bundles on an algebraic surface. Ann. Math.106, 45–60 (1977)Google Scholar
  8. [H]
    Hartshorne, R.: Algebraic Geometry. (Grad. Texts Math., vol. 52) Berlin Heidelberg New York: Springer 1977Google Scholar
  9. [Hi, Hu]
    Hirschowitz, A., Hulek, K.: Complete families of stable bundles over ℙ2. (Lect. Notes Math., vol. 1194, pp. 19–33) Berlin Heidelberg New York: Springer 1990Google Scholar
  10. [Hu]
    Hulek, K.: Stable rank-2 vector bundles on ℙ2 withc 1 odd. Math. Ann.242, 241–266 (1979)Google Scholar
  11. [Hu, S]
    Hulek, K., Strømme, S.A.: Appendix to the paper “Complete families of stable vector bundles over ℙ2. (Lect. Notes Math., vol. 1194, pp 34–40) Berlin Heidelberg New York: Springer 1980Google Scholar
  12. [Hu, LP]
    Hulek, K., Le Potier, J.: Sur l'espace de modules des faisceaux semistables de rang 2 de class de Chern (0, 3) sur ℙ2. Ann. Inst. Fourier39, 251–292 (1989)Google Scholar
  13. [H]
    Huybrechts, D.: Stabile Vektorbündel auf algebraischen Flächen. Tyurins Methode zum Studium der Geometrie der Modulräume. Thesis (1992)Google Scholar
  14. [L]
    Li, J.: Algebraic Geometric interpretation of Donaldson's polynomial invariants of algebraic surfaces. Preprint (1992)Google Scholar
  15. [L2]
    Li, J.: Kodaira dimension of moduli spaces of vector bundles on surfaces. Preprint (1992)Google Scholar
  16. [LP]
    Le Potier, J.: Sur le groupe de Picard de l'espace de modules de fibrés stables sur ℙ2. Ann. Sci. Éc. Norm. Supér., IV. Sér.14, 141–155 (1981)Google Scholar
  17. [Ma]
    Maruyama, M.: Moduli of stable sheaves I. J. Math. Jap.17, 91–126 (1977)Google Scholar
  18. [M, R]
    Mehta, V.B., Ramanathan, A.: Restriction of stable sheaves and representation of the fundamental group. Invent. Math.77, 163–172 (1984)Google Scholar
  19. [Mu]
    Mukai, S.: Symplectic structure on the moduli space of sheaves on an Abelian and K3-surface. Invent. Math.77, 101–116 (1984)Google Scholar
  20. [GIT]
    Mumford, D., Fogarty, J.: Geometric invariant theory. (Ergeb. Math. Grenzgeb., 2. Folge vol. 34) Berlin Heidelberg New York: Springer 1982Google Scholar
  21. [O'G1]
    O'Grady, K.: Algebro geometric analogoues of Donaldson's polynomials. Invent. Math.107, 1992Google Scholar
  22. [O'G2]
    O'Grady, K.: The irreducible components of moduli spaces of vector bundles on surfaces. Preprint (1992)Google Scholar
  23. [Q]
    Qin, Z.: Birational properties of moduli spaces of stable locally free rank-2 sheaves on algebraic surfaces. Preprint (1991)Google Scholar
  24. [St]
    Strømme, S.A.: Ample divisors on fine moduli spaces on the projective plane. Math. Z.187, 405–423 (1987)Google Scholar
  25. [T]
    Tyurin, A.N.: The moduli space of vector bundles on threefolds, surfaces and curves. Preprint (1990)Google Scholar
  26. [Z]
    Zuo, K.: Generic smoothness of the moduli of rank two stable bundles over an algebraic surface. MPI-Preprint 7 (1990)Google Scholar

Copyright information

© Springer-Verlag 1994

Authors and Affiliations

  • D. Huybrechts
    • 1
  1. 1.Max-Planck-Institut für MathematikBonnGermany

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