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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

Citations:

Zbl 1006.32020
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