Ramifications, Reduction of Singularities, Separatrices
| dc.creator | Ayuso, Pedro Fortuny | |
| dc.date | 2001-11-22 | |
| dc.date | 2002-06-03 | |
| dc.date.accessioned | 2026-07-07T04:44:44Z | |
| dc.date.available | 2026-07-07T04:44:44Z | |
| dc.description | We study the behaviour of sequences of blowing-ups under ramifications, and use the results to give a simple proof of Camacho-Sad's Theorem on the existence of Separatrices for singularities of plane holomorphic foliations. The main result we prove is that for any finite sequence $π$ of blowing-ups, there is a ramification morphism $ρ$ such that the elimination of indeterminations $\tildeπ$ of $π^{-1}\circ ρ$ is a sequence of blowing-ups \emph{with centers at regular points of the exceptional divisors}; moreover, we show that if $π$ is the reduction of singularities of a foliation $\mathcal{F}$, then $ρ$ can be such that $\tildeπ^{\star}ρ^{\star}\mathcal{F}$ has only simple singularities. | |
| dc.description | 7 pages, uses amsxtra and xy. Previous version was erroneous | |
| dc.identifier | https://arxiv.org/abs/math/0111244 | |
| dc.identifier | http://arxiv.org/abs/math/0111244 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/62710 | |
| dc.subject | Dynamical Systems | |
| dc.title | Ramifications, Reduction of Singularities, Separatrices | |
| dc.type | text |