Big vector bundles and complex manifolds with semi-positive tangent bundles

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• 作者：Xiaokui Yang
• 关键词：Mathematics Subject Classification53C55 ; 32J25 ; 32L15 ; 14J15
• 刊名：Mathematische Annalen
• 出版年：2017
• 出版时间：February 2017
• 年：2017
• 卷：367
• 期：1-2
• 页码：251-282
• 全文大小：
• 刊物类别：Mathematics and Statistics
• 刊物主题：Mathematics, general;
• 出版者：Springer Berlin Heidelberg
• ISSN：1432-1807
• 卷排序：367

文摘

We classify compact Kähler manifolds with semi-positive holomorphic bisectional and big tangent bundles. We also classify compact complex surfaces with semi-positive tangent bundles and compact complex 3-folds of the form \({\mathbb P}(T^*X)\) whose tangent bundles are nef. Moreover, we show that if X is a Fano manifold such that \({\mathbb P}(T^*X)\) has nef tangent bundle, then \(X\cong {\mathbb P}^n\).