On transcendental automorphisms of algebraic foliations

B. Scárdua. "On transcendental automorphisms of algebraic foliations." Fundamenta Mathematicae 179.2 (2003): 179-190. <http://eudml.org/doc/282732>.

@article{B2003,
abstract = {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.},
author = {B. Scárdua},
journal = {Fundamenta Mathematicae},
keywords = {isomorphisms; holomorphic foliation; singularities on a complex manifold},
language = {eng},
number = {2},
pages = {179-190},
title = {On transcendental automorphisms of algebraic foliations},
url = {http://eudml.org/doc/282732},
volume = {179},
year = {2003},
}

TY - JOUR
AU - B. Scárdua
TI - On transcendental automorphisms of algebraic foliations
JO - Fundamenta Mathematicae
PY - 2003
VL - 179
IS - 2
SP - 179
EP - 190
AB - 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.
LA - eng
KW - isomorphisms; holomorphic foliation; singularities on a complex manifold
UR - http://eudml.org/doc/282732
ER -