2001/11/22 by Pedro Fortuny Ayuso, Ayuso, Pedro Fortuny
Computer Science · Mathematics · #Advanced Differential Equations and Dynamical Systems #Dynamical Systems (math.DS) #FOS: Mathematics #Holomorphic and Operator Theory #Polynomial and algebraic computation #math.DS
paper · pdf · doi:10.48550/arxiv.math/0111244
7 pages, uses amsxtra and xy. Previous version was erroneous
openalex publication_date 2001/11/22 · arxiv created 2002/06/03 · arxiv updated 2009/11/30 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
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 π of π-1∘ ρ is a sequence of blowing-ups with centers at regular points of the exceptional divisors; moreover, we show that if π is the reduction of singularities of a foliation F, then ρ can be such that π⋆ρ⋆F has only simple singularities.