论文标题
封闭的杂型1形
Closed meromorphic 1-forms
论文作者
论文摘要
我们回顾了封闭的Meromorthic $ 1 $形式的属性以及它们所定义的叶子的属性。我们介绍并解释了叶叶理论的经典结果，例如索引定理，分离的存在以及在封闭的meromorphic $ 1 $ forms和平坦的meromororphic连接的镜头下的奇异性分辨率。我们应用该理论来研究半全球环境（叶片奇异集中包含的紧凑曲线的邻域）中的代数分离，以及在紧凑型kähler歧管上具有数值琐碎的正常束的光滑超丘面的几何形状。
We review properties of closed meromorphic $1$-forms and of the foliations defined by them. We present and explain classical results from foliation theory, like index theorems, the existence of separatrices, and resolution of singularities under the lenses of the theory of closed meromorphic $1$-forms and flat meromorphic connections. We apply the theory to investigate the algebraicity separatrices in a semi-global setting (neighborhood of a compact curve contained in the singular set of the foliation), and the geometry of smooth hypersurfaces with numerically trivial normal bundle on compact Kähler manifolds.
