A Generalization of the Kodaira Vanishing and Embedding Theorem

1995/02/02 by Zhu, Ying
#Algebraic Geometry (math.AG) #Differential Geometry (math.DG) #FOS: Mathematics

paper · doi:10.48550/arxiv.alg-geom/9502002

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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