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.
@article{bwmeta1.element.bwnjournal-article-doi-10_4064-fm179-2-5,
author = {B. Sc\'ardua},
title = {On transcendental automorphisms of algebraic foliations},
journal = {Fundamenta Mathematicae},
volume = {177},
year = {2003},
pages = {179-190},
zbl = {1047.37033},
language = {en},
url = {http://dml.mathdoc.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-fm179-2-5}
}
B. Scárdua. On transcendental automorphisms of algebraic foliations. Fundamenta Mathematicae, Tome 177 (2003) pp. 179-190. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-fm179-2-5/