Skip to main content
Log in

Γ-type-invariants associated toPU(2)-bundles and the differentiable structure of Barlow's surface

  • Published:
Inventiones mathematicae Aims and scope

This is a preview of subscription content, log in via an institution to check access.

Access this article

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

References

  • [B] Barlow, R.: A simply connected surface of general type withp g=0. Invent. Math.79, 293–301 (1985)

    Google Scholar 

  • [BPV] Barth, W., Peters, C., Van de Ven, A.: Compact complex surfaces. (Erg. Math. (3), Vol. 4). Berlin-Heidelberg-New York: Springer 1984

    Google Scholar 

  • [DW] Dold, A., Whitney, H.: Classification of oriented sphere bundles over a 4-complex. Ann. Math. (2)69, 667–677 (1959)

    Google Scholar 

  • [Do1] Donalson, S.K.: Anti-self-dual Yang-Mills connections over an algebraic surface and stable vector bundles. Proc. Lond. Math. Soc. (3)50, 1–26 (1985)

    Google Scholar 

  • [Do2] Donaldson, S.K.: Irrationality and theh-cobordism conjecture. J. Differ. Geom.26, 141–168 (1987)

    Google Scholar 

  • [Do3] Donaldson, S.K.: Polynomial invariants for smooth four manifolds. Preprint Oxford (1987)

  • [FM1] Friedman, R., Morgan, J.: On the diffeomorphism types of certain algebraic surfaces: J. Differ. Geom.27, 297–369 (1988)

    Google Scholar 

  • [FM2] Friedman, R., Morgan, J.: Algebraic surfaces and 4-manifolds: some conjectures and speculations. Bull. Am. Math. Soc.18, 1–19 (1988)

    Google Scholar 

  • [FS] Fintushel, R., Stern, R.J.:SO(3)-connections and the topology of 4-manifolds. J. Differ. Geom.20, 523–529 (1984)

    Google Scholar 

  • [FU] Freed, D.S., Uhlenbeck, K.K.: Instantons and four-manifolds. (M.S.R.I. Publ., Vol. 1). Berlin-Heidelberg-New York: Springer 1984

    Google Scholar 

  • [HH] Hirzebruch, F., Hopf, H.: Felder von Flächenelementen in 4-dimensionalen Mannigfaltigkeiten. Math. Ann.136, 156–172 (1958)

    Google Scholar 

  • [K] Kobayashi, S.: Differential geometry of complex vector bundles. I. Shoten and Princeton University Press 1987

  • [Ko] Kotschick, D.: On manifolds homeomorphic to\(\mathbb{C}P^2 \# 8\overline {\mathbb{C}P^2 } \). Invent. Math.95, 591–600 (1989)

    Google Scholar 

  • [LO] Lübke, M., Okonek, C.: Moduli spaces of simple bundles and Hermitian-Einstein connections. Math. Ann.276, 663–674 (1987)

    Google Scholar 

  • [Ma] Maruyama, M.: Moduli of stable sheaves II. J. Math. Kyoto18, 557–614 (1978)

    Google Scholar 

  • [Mi] Miyaoka, Y.: Tricanonical maps of numerical Godeaux surfaces. Invent. Math.34, 99–111 (1976)

    Google Scholar 

  • [OV] Okonek, C.: Van de Ven, A., Stable bundles and differentiable structures on certain elliptic surfaces. Invent. Math.86, 357–370 (1986)

    Google Scholar 

  • [UY] Uhlenbeck, K.K., Yau, S.-T.: On the existence of Hermitian-Yang-Mills connections in stable vector bundles. Commun. Pure Appl. Math.39, 257–293 (1986)

    Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Additional information

Supported by a Heisenberg-scholarship of the DFG

Supported by the M.P.I. Bonn

Rights and permissions

Reprints and permissions

About this article

Cite this article

Okonek, C., Van de Ven, A. Γ-type-invariants associated toPU(2)-bundles and the differentiable structure of Barlow's surface. Invent Math 95, 601–614 (1989). https://doi.org/10.1007/BF01393893

Download citation

  • Issue Date:

  • DOI: https://doi.org/10.1007/BF01393893

Keywords

Navigation