On transcendental automorphisms of algebraic foliations

• Autorzy: B. Scárdua
• Języki publikacji: EN

Abstrakty

EN

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.

Kategorie tematyczne

• 37F75: Holomorphic foliations and vector fields
• 32S65: Singularities of holomorphic vector fields and foliations

• Wydawca: Institute of Mathematics Polish Academy of Sciences
• Czasopismo: Fundamenta Mathematicae
• Rocznik: 2003
• Tom: 179
• Numer: 2
• Strony: 179-190

Daty

wydano

2003

Twórcy

autor

B. Scárdua

• Instituto de Matemática, Universidade Federal do Rio de Janeiro, C.P. 68530, CEP. 21945-970 Rio de Janeiro, RJ, Brazil

Identyfikatory

DOI

10.4064/fm179-2-5