Kodaira消隐嵌入定理的推广
A Generalization of the Kodaira Vanishing and Embedding Theorem
摘要：
本文将Kähler流形的Kodaira消失定理和嵌入定理推广到相关的线丛有一个小的负曲率区域的情形。为了证明消失定理，我们适应技术Elworthy-Rosenberg消失定理在黎曼几何。对于嵌入定理，我们证明了一个Kähler流形与大多是积极的线丛是Moishezon，因为通常的爆破技术不工作，在我们的情况。
英文摘要：
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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