论文标题
通过曲线奇异的全态叶子。 iii：零轻的数字
Singular holomorphic foliations by curves. III: Zero Lelong numbers
论文作者
论文摘要
令$ \ mathcal {f} $为曲线的圆形叶面，以$ 0 $ in $ \ mathbb {c}^n $（$ n \ geq 2 $）为$ 0 $的曲线定义为具有$ 0 $的$ 0 $。令$ t $为$ \ mathcal {f} $指导的正谐波电流，它不会给任何$ n $坐标不变的超级平面$ \ {z_j = 0 \} $ for $ 1 \ leq j \ leq j \ leq n。此外，给出了该本地结果在全球上下文中的应用。我们还讨论了几个基本概念（例如定向的正谐电流），定向DDC封闭电流，lelong数字等之间的关系。
Let $\mathcal{F}$ be a holomorphic foliation by curves defined in a neighborhood of $0$ in $\mathbb{C}^n$ ($n\geq 2$) having $0$ as a weakly hyperbolic singularity. Let $T$ be a positive harmonic current directed by $\mathcal{F}$ which does not give mass to any of the $n$ coordinate invariant hyperplanes $\{z_j=0\}$ for $1\leq j\leq n.$ Then we show that the Lelong number of $T$ at $0$ vanishes. Moreover, an application of this local result in the global context is given. We discuss also the relation between several basic notions such as directed positive harmonic currents, directed positive ddc-closed currents, Lelong numbers etc. in the framework of singular holomorphic foliations.
