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Communications in Mathematical Physics

, Volume 129, Issue 3, pp 525–534 | Cite as

The\(\bar \partial \)-operator on algebraic curves

  • Jochen Brüning
  • Norbert Peyerimhoff
  • Herbert Schröder
Article

Abstract

For a singular algebraic curve we show that all closed extensions of\(\bar \partial \) are Fredholm, and we give a general index formula. In particular, we prove a modified version of a conjecture due to MacPherson.

Keywords

Neural Network Statistical Physic Complex System Nonlinear Dynamics Quantum Computing 
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References

  1. [B] Brüning, J.:L 2-index theorems on certain complete manifolds. To appear in J. Differ. Geom.Google Scholar
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  6. [McP] MacPherson, R.: Global questions in the topology of singular spaces. Proceedings of the International Congress of Mathematicians, August 16–24, 1983, Warszawa, Vol. 1, pp. 213–235. Warszawa: Polish Scientific Publishers 1984Google Scholar
  7. [P] Pardon, W.: TheL 2-\(\bar \partial \)-cohomology of an algebraic surface (to appear)Google Scholar

Copyright information

© Springer-Verlag 1990

Authors and Affiliations

  • Jochen Brüning
    • 1
  • Norbert Peyerimhoff
    • 1
  • Herbert Schröder
    • 1
  1. 1.Institut für MathematikUniversität AugsburgAugsburgFederal Republic of Germany

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