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On transcendental automorphisms of algebraic foliations

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Scárdua B.

Fundamenta Mathematicae

2003

tom 179

nr 2

179-190

We study the group Aut(ℱ) of (self) isomorphisms of a holomorphic foliation ℱ with singularities on a complex manifold. We prove, for instance, that for a polynomial foliation on ℂ² this group consists of algebraic elements provided that the line at infinity ℂP(2)∖ℂ² is not invariant under the foliation. If in addition ℱ is of general type (cf. [20]) then Aut(ℱ) is finite. For a foliation with hyperbolic singularities at infinity, if there is a transcendental automorphism then the foliation is either linear logarithmic, Riccati or chaotic (cf. Definition 1). We also give a description of foliations admitting an invariant algebraic curve C ⊂ ℂ² with a transcendental foliation automorphism.

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1 Fundamenta Mathematicae

1 Scárdua B.

1 2003

Wyniki wyszukiwania

On transcendental automorphisms of algebraic foliations