Bogomolov和McQuillan之后的有理连通叶理
Rationally connected foliations after Bogomolov and McQuillan
摘要：
本文给出了正规簇上给定的叶理具有代数有理连通叶的充分判据。根据Bogomolov-McQuillan的预印本中的思想，并利用Langer和Graber-Harris-Starr最近的作品，我们给出了以前结果的一个干净、简短和简单的证明。除了一个新的消灭定理的向量丛的正特征，我们的证明只采用标准的技术森理论，并没有作出任何参考的更多涉及的属性的叶状特征p.我们应用的结果表明，Q-Fano品种不稳定的切丛总是承认一个序列的部分合理的concurents自然与哈德-Narasimhan过滤。
英文摘要：
This paper is concerned with a sufficient criterion to guarantee that a given foliation on a normal variety has algebraic and rationally connected leaves. Following ideas from a preprint of Bogomolov-McQuillan and using recent works of Langer and Graber-Harris-Starr, we give a clean, short and simple proof of previous results. Apart from a new vanishing theorem for vector bundles in positive characteristic, our proof employs only standard techniques of Mori theory and does not make any reference to the more involved properties of foliations in characteristic p. We apply the result to show that Q-Fano varieties with unstable tangent bundles always admit a sequence of partial rational quotients naturally associated to the Harder-Narasimhan filtration.
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