Holomorphic Lefschetz formula for manifolds with boundary


Тип публикации: статья из журнала

Год издания: 2004

Идентификатор DOI: 10.1007/s00209-003-0612-1

Аннотация: The classical Lefschetz fixed point formula expresses the number of fixed points of a continuous map f : M-->M in terms of the transformation induced by f on the cohomology of M. In 1966 Atiyah and Bott extended this formula to elliptic complexes over a compact closed manifold. In particular, they presented a holomorphic Lefschetz Показать полностьюformula for compact complex manifolds without boundary, a result, in the framework of algebraic geometry due to Eichler (1957) for holomorphic curves. On compact complex manifolds with boundary the Dolbeault complex is not elliptic, hence the Atiyah-Bott theory is no longer applicable. To get rid of the difficulties related to the boundary behaviour of the Dolbeault cohomology, Donelli and Fefferman (1986) derived a fixed point formula for the Bergman metric. The purpose of this paper is to present a holomorphic Lefschetz formula on a strictly convex domain in C-n, n>1.

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Журнал: Mathematische Zeitschrift

Выпуск журнала: Vol. 246, Is. 4

Номера страниц: 769-794

ISSN журнала: 00255874

Место издания: New York

Издатель: Springer-Verlag


  • Kytmanov A. (Krasnoyarsk State University)
  • Myslivets S. (Krasnoyarsk State University)
  • Tarkhanov N. (Universitat Potsdam,Institut fur Mathematik)

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