The\(\bar \partial \)-operator on algebraic curves
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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.
KeywordsNeural Network Statistical Physic Complex System Nonlinear Dynamics Quantum Computing
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- [B] Brüning, J.:L 2-index theorems on certain complete manifolds. To appear in J. Differ. Geom.Google Scholar
- [dC] doCarmo, M.: Differential geometry of curves and surfaces. Englewood Cliffs, NJ: Prentice Hall 1976Google Scholar
- [Gi] Gilkey, P.: Invariance theory, the heat equation, and the Atiyah-Singer index theorem. Wilmington, DE: Publish or Perish 1984Google Scholar
- [G+H] Griffiths, P., Harris, J.: Principles of algebraic geometry. New York: Wiley 1978Google Scholar
- [H] Hirzebruch, F.: Neue topologische Methoden in der algebraischen Geometrie. Berlin, Göttingen, Heidelberg: Springer 1956Google Scholar
- [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
- [P] Pardon, W.: TheL 2-\(\bar \partial \)-cohomology of an algebraic surface (to appear)Google Scholar