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Holomorphic Lefschetz fixed point formula for non-compact Kähler manifolds

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Abstract

The authors obtain a holomorphic Lefschetz fixed point formula for certain non-compact “hyperbolic” Kähler manifolds (e.g. Kähler hyperbolic manifolds, bounded domains of holomorphy) by using the Bergman kernel. This result generalizes the early work of Donnelly and Fefferman.

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References

  1. Chen, B. Y., Infinite dimensionality of the middle L 2-cohomology on non-compact Kähler hyperbolic manifolds, Publ. RIMS., 42, 2006, 683–689.

    Article  MATH  Google Scholar 

  2. Donnelly, H. and Fefferman, C., Fixed point formula for the Bergman kernel, Amer. J. Math., 108, 1986, 1241–1257.

    Article  MATH  MathSciNet  Google Scholar 

  3. Donnelly, H. and Fefferman, C., L 2 cohomology and index theorem for the Bergman metric, Ann. Math., 118, 1983, 593–618.

    Article  MathSciNet  Google Scholar 

  4. Fefferman, C., The Bergman kernel and biholomorphic mappings of pseudoconvex domains, Invent. Math., 26, 1974, 1–65.

    Article  MATH  MathSciNet  Google Scholar 

  5. Gromov, M., Kähler hyperbolicity and L 2-Hodge theory, J. Diff. Geom., 33, 1991, 263–292.

    MATH  MathSciNet  Google Scholar 

  6. Hörmander, L., L 2 estimates and existence theorems for the \( \bar \partial \) operator, Acta Math., 113, 1965, 89–152.

    Article  MATH  MathSciNet  Google Scholar 

  7. Kerzman, N., The Bergman kernel function. Differentiability at the boundary, Math. Ann., 195, 1972, 149–158.

    Article  MathSciNet  Google Scholar 

  8. Lefschetz, S., Intersections and transformations of complexes and manifolds, Trans. Amer. Math. Soc., 28, 1926, 1–49.

    Article  MATH  MathSciNet  Google Scholar 

  9. McNeal, J. D., L 2 harmonic forms on some complete Kähler manifolds, Math. Ann., 323, 2002, 319–349.

    Article  MATH  MathSciNet  Google Scholar 

  10. Oeljeklaus, K., Pflug, P. and Youssfi, E. H., The Bergman kernel of the minimal ball and applications, Ann. Inst. Fourier., 47, 1997, 915–928.

    MATH  MathSciNet  Google Scholar 

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Authors and Affiliations

  1. Department of Mathematics, Tongji University, Shanghai, 200092, China

    Boyong Chen

  2. Department of Mathematics, Zhejiang Normal University, Jinhua, 321004, Zhejiang, China

    Yang Liu

Authors
  1. Boyong Chen
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  2. Yang Liu
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Corresponding author

Correspondence to Yang Liu.

Additional information

Project supported by the Program for New Century Excellent Talents in University of China (No. 050380), the Grant for Chinese Excellent Doctorate’s Degree Thesis (No. 200519), the Fok Ying Tung Education Foundation and the National Natural Science Foundation of China (No. 10871145).

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Chen, B., Liu, Y. Holomorphic Lefschetz fixed point formula for non-compact Kähler manifolds. Chin. Ann. Math. Ser. B 29, 679–686 (2008). https://doi.org/10.1007/s11401-007-0256-2

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  • DOI: https://doi.org/10.1007/s11401-007-0256-2

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