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A Generalization of the Kodaira Vanishing and Embedding Theorem

Ying Zhu
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Abstract

We give several generalizations of the Kodaira vanishing and embedding theorems for Kähler manifolds to the case where the relevent line bundle has a small region of negative curvature. To prove the vanishing theorems we adapt techniques of Elworthy-Rosenberg for vanishing theorems in Riemannian geometry. For the embedding theorem, we show that a Kähler manifold with a mostly positive line bundle is Moishezon, since the usual blow up techniques do not work in our situation.

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BibTeXRIS

Ying Zhu. 1995-02-02. A Generalization of the Kodaira Vanishing and Embedding Theorem. https://arxiv.org/abs/alg-geom/9502002

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