Entire curves and holomorphic foliations. (Courbes entières et feuilletages holomorphes.)(French)Zbl 1004.32011

From the introduction: The underlying paper concerns a discussion and ‘introduction’ to the paper of M. McQuillan [Publ. Math., Inst. Hautes Etud. Sci. 87, 121-174 (1998; Zbl 1006.32020)] with special attention to the ‘foliated’ part in the cited paper.
The following result is provd: Theorem: Let $${\mathcal F}$$ be a holomorphic foliation of $$\mathbb{C}\mathbb{P}^2$$ of degree $$d\geq 5$$. Suppose each singularity of $${\mathcal F}$$ is nonnilpotent, i.e. locally generated by a vector field whose linear part is nonnilpotent. Then each holomorphic mapping $$f:\mathbb{C}\to\mathbb{C}\mathbb{P}^2$$ tangential of $${\mathcal F}$$ is degenerated.

MSC:

 32S65 Singularities of holomorphic vector fields and foliations 32H25 Picard-type theorems and generalizations for several complex variables

Zbl 1006.32020