论文标题
消失的定理，有理联系和中间阳性
Vanishing theorems, rational connectedness and intermediate positivity
论文作者
论文摘要
We establish a vanishing theorem for uniformly RC $k$-positive Hermitian holomorphic vector bundles, and show that the holomorphic tangent bundle of a compact complex manifold equipped with a positive $k$-Ricci curvature Kähler metric (or more generally a positive $k$-Ricci curvature Kähler-like Hermitian metric) is uniformly RC $k$-positive.提出了两个主要应用。第一个是推断出在Kähler或Hermitian歧管上的一些全体形态张量场的空间是微不足道的，从而推广了一些最新结果。第二个是表明，紧凑的Kähler歧管，其全体形状切线束可以赋予一个均匀的RC $ K $ k $阳性的Hermitian公制或正$ K $ -RICCI弯曲曲率的Hermitian Like Hermitian Like Like Hermitian指标是投影和合理连接的。
We establish a vanishing theorem for uniformly RC $k$-positive Hermitian holomorphic vector bundles, and show that the holomorphic tangent bundle of a compact complex manifold equipped with a positive $k$-Ricci curvature Kähler metric (or more generally a positive $k$-Ricci curvature Kähler-like Hermitian metric) is uniformly RC $k$-positive. Two main applications are presented. The first one is to deduce that spaces of some holomorphic tensor fields on such Kähler or Hermitian manifolds are trivial, generalizing some recent results. The second one is to show that a compact Kähler manifold whose holomorphic tangent bundle can be endowed with either a uniformly RC $k$-positive Hermitian metric or a positive $k$-Ricci curvature Kähler-like Hermitian metric is projective and rationally connected.
