论文标题
几乎是NEF的常规叶子和Fujita的反身滑轮的分解
Almost nef regular foliations and Fujita's decomposition of reflexive sheaves
论文作者
论文摘要
在本文中，我们研究了几乎NEF的常规叶子。我们提供了一个平稳的投影品种$ x $的结构定理，几乎是nef常规叶子$ \ Mathcal {f} $：$ x $承认平滑的形态$ f：x \ rightarrow y $，具有合理连接的纤维，因此$ \ nathcal {f} $是数字上常规的$ y $ y $ y $ y $ y $ y $ y $ y $ $ y $ $ y $ $。此外，$ f $的特征是$ \ Mathcal {f} $的代数部分的相对MRC纤维。作为推论，几乎合理连接的品种的几乎NEF切线束通常足够丰富。为了证明，我们概括了藤田的分解定理。作为副产品，我们表明$ f _ {*}（mk_ {x/y}）$的反身壳是遗传式平坦矢量束的直接总和，并且对于任何代数纤维空间$ f：x \ rightarrow y $。我们还使用NEF抗典型捆绑包研究叶子。
In this paper, we study almost nef regular foliations. We give a structure theorem of a smooth projective variety $X$ with an almost nef regular foliation $\mathcal{F}$: $X$ admits a smooth morphism $f: X \rightarrow Y$ with rationally connected fibers such that $\mathcal{F}$ is a pullback of a numerically flat regular foliation on $Y$. Moreover, $f$ is characterized as a relative MRC fibration of an algebraic part of $\mathcal{F}$. As a corollary, an almost nef tangent bundle of a rationally connected variety is generically ample. For the proof, we generalize Fujita's decomposition theorem. As a by-product, we show that a reflexive hull of $f_{*}(mK_{X/Y})$ is a direct sum of a hermitian flat vector bundle and a generically ample reflexive sheaf for any algebraic fiber space $f : X \rightarrow Y$. We also study foliations with nef anti-canonical bundles.
