Vector fields and foliations associated to groups of projective automorphisms
| dc.creator | Santos, Fabio H. | |
| dc.creator | Scardua, Bruno | |
| dc.date | 2007-09-04 | |
| dc.date.accessioned | 2026-07-07T08:27:42Z | |
| dc.date.available | 2026-07-07T08:27:42Z | |
| dc.description | We 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.description | 25 pages | |
| dc.identifier | https://arxiv.org/abs/0709.0546 | |
| dc.identifier | http://arxiv.org/abs/0709.0546 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/137358 | |
| dc.subject | Complex Variables | |
| dc.subject | Dynamical Systems | |
| dc.subject | 37F75, 32M25, 32S65 | |
| dc.title | Vector fields and foliations associated to groups of projective automorphisms | |
| dc.type | text |