论文标题
一些Kollar-Enoki类型的注射率和Nadel类型在紧凑的Kahler歧管上消失的定理
Some Kollar-Enoki type injectivity and Nadel type vanishing theorems on compact Kahler manifolds
论文作者
论文摘要
在本文中，我们将首先通过使用Hodge理论，Bochner- Kodaira-Nakano身份以及O. Fujino和S. matsumura在[15、25、25、36、39]中提供的分析方法，首先展示一些有关紧凑型卡勒歧管的Kollar-Enoki类型注射定理。我们有一些直接的推论。特别是，我们将证明我们的主要注射率定理意味着在光滑的投射歧管上定理的几种Nadel型消失。 Second, by applying the transcendental method, especially the Demailly-Peternell-Schneider equisingular approximation theorem and the Hormander L2 estimates, we will prove some Nakano-Demailly type and Nadel type vanishing theorems for holomorphic vector bundles on compact Kahler manifolds, twisted by pseudo-effective line bundles and multiplier ideal sheaves.作为应用程序，我们将证明我们的第一个主要消失定理将古典中的中玛利·德米利（Nakano-Demailly）消失了，而第二个则包含著名的纳德尔（Nadel）消失定理作为特殊情况。
In this paper we will first show some Kollar-Enoki type injectivity theorems on compact Kahler manifolds, by using the Hodge theory, the Bochner- Kodaira-Nakano identity and the analytic method provided by O. Fujino and S. Matsumura in [15, 25, 36, 39]. We have some straightforward corollaries. In particular, we will show that our main injectivity theorem implies several Nadel type vanishing theorems on smooth projective manifolds. Second, by applying the transcendental method, especially the Demailly-Peternell-Schneider equisingular approximation theorem and the Hormander L2 estimates, we will prove some Nakano-Demailly type and Nadel type vanishing theorems for holomorphic vector bundles on compact Kahler manifolds, twisted by pseudo-effective line bundles and multiplier ideal sheaves. As applications, we will show that our first main vanishing theorem generalizes the classical Nakano-Demailly vanishing theorem while the second one contains the famous Nadel vanishing theorem as a special case.
