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Riemann-Roch Theorem for Strongly Pseudoconvex Manifolds of Dimension Three

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Several Complex Variables

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Abstract

It is generally expected that an analogous formula of Riemann-Roch holds for strongly psudoconvex manifolds of arbitrary dimensions. In dimension two such a formula for integral divisors was derived by Kato ([1]). In this short note, we shall extend this formula to three dimensions.

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References

  1. Kato, M., Riemann-Roch theorem for strongly pseudoconvex manifolds of dimensions 2., Math. Ann. 222, 243–250 (1976).

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  2. Laufer, H., On rational singularities. Amer. J. Math. 94, 597–608 (1972).

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  3. Siu, Y.-T., Absolute gap-sheaves and extensions of coherent analytic sheaves. Trans. Amer. Math. Soc. 141, 361–376 (1969)

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Authors
  1. Paul C.-P. Yang
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  2. Stephen S.-T. Yau
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Editor information

Editors and Affiliations

  1. Department of Mathematics, Princeton University, 08544, Princeton, NJ, USA

    J. J. Kohn

  2. Mathematisches Institüt der Universität, Einstein-strasse 64, D-4400, Münster, Germany

    R. Remmert

  3. Acadima Sinica, Beijing, China

    Q.-K. Lu

  4. Department of Mathematics, Harvard University, 02138, Cambridge, MA, USA

    Y.-T. Siu

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© 1984 Birkhäuser Boston, Inc.

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Yang, P.CP., Yau, S.ST. (1984). Riemann-Roch Theorem for Strongly Pseudoconvex Manifolds of Dimension Three. In: Kohn, J.J., Remmert, R., Lu, QK., Siu, YT. (eds) Several Complex Variables. Birkhäuser Boston. https://doi.org/10.1007/978-1-4612-5296-2_30

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  • DOI: https://doi.org/10.1007/978-1-4612-5296-2_30

  • Publisher Name: Birkhäuser Boston

  • Print ISBN: 978-0-8176-3189-5

  • Online ISBN: 978-1-4612-5296-2

  • eBook Packages: Springer Book Archive

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