Vector fields and foliations associated to groups of projective automorphisms

dc.creatorSantos, Fabio H.
dc.creatorScardua, Bruno
dc.date2007-09-04
dc.date.accessioned2026-07-07T08:27:42Z
dc.date.available2026-07-07T08:27:42Z
dc.descriptionWe introduce and give normal forms for (one-dimensional) Riccati foliations (vector fields) on $\ov \bc \times \bc P(2)$ and $\ov \bc \times \ov \bc^n$. These are foliations are characterized by transversality with the generic fiber of the first projection and we prove they are conjugate {\em in some invariant Zariski open subset} to the suspension of a group of automorphisms of the fiber, $\bc P(2)$ or $\ov \bc^n$, this group called {\it global holonomy}. Our main result states that given a finitely generated subgroup $G$ of $\Aut(\bc P (2))$, there is a Riccati foliation on $\ov \bc \times \bc P(2)$ for which the global holonomy is conjugate to $G$.
dc.description25 pages
dc.identifierhttps://arxiv.org/abs/0709.0546
dc.identifierhttp://arxiv.org/abs/0709.0546
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/137358
dc.subjectComplex Variables
dc.subjectDynamical Systems
dc.subject37F75, 32M25, 32S65
dc.titleVector fields and foliations associated to groups of projective automorphisms
dc.typetext

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