On a neighborhood of a torus leaf of a certain class of holomorphic foliations on complex surfaces

Abstract

Let $C$ be a smooth elliptic curve embedded in a smooth complex surface $X$ such that $C$ is a leaf of a suitable holomorphic foliation of $X$. We investigate complex analytic properties of a neighborhood of $C$ under some assumptions on complex dynamical properties of the holonomy function. As an application, we give an example of $(C,X)$ in which the line bundle $[C]$ is formally flat along $C$ however it does not admit a $C^{\infty }$ Hermitian metric with semi-positive curvature.

12 pages

References in corpus (2)

• On the minimality of canonically attached singular Hermitian metrics on certain nef line bundles
• On minimal singular metrics of certain class of line bundles whose section ring is not finitely generated