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Ein einfacher Beweis des Verschwindungssatzes für positive holomorphe Vektorraumbündel

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Abstract

The object of this note is to give a simple proof of the following vanishing theorem of le Potier [8]: Let X be a compact complex manifold of dimension n and E a weakly positive holomorphic vector bundle of rank r on X. Then

$$H^q (X,\Omega ^p (E)) = 0forp + q \geqslant n + r.$$

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  1. Fachbereich Mathematik der Universität, Universitätsstraße 31, 84 Regensburg

    Michael Schneider

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  1. Michael Schneider
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Herrn W. Thimm zum 60. Geburtstag gewidmet

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Schneider, M. Ein einfacher Beweis des Verschwindungssatzes für positive holomorphe Vektorraumbündel. Manuscripta Math 11, 95–101 (1974). https://doi.org/10.1007/BF01189093

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  • DOI: https://doi.org/10.1007/BF01189093

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