A Generalization of the Kodaira Vanishing and Embedding Theorem

Details A Generalization of the Kodaira Vanishing and Embedding Theorem A Generalization of the Kodaira Vanishing and Embedding Theorem

1995-02-02

arxiv.org/abs/alg-geom/9502002v1

Mathematics

Algebraic Geometry

21 pages, amslatex postscript file

Scientific paper

We give several generalizations of the Kodaira vanishing and embedding theorems for K\"ahler 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 K\"ahler 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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