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arXiv · 1510.02287

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

Takayuki Koike
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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.

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Takayuki Koike. 2015-10-08. On a neighborhood of a torus leaf of a certain class of holomorphic foliations on complex surfaces. https://arxiv.org/abs/1510.02287

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