2017/08/02 by Cuzzuol, Gilberto, Mol, Rogério
#32S65 #37F75 #Complex Variables (math.CV) #Dynamical Systems (math.DS) #FOS: Mathematics
paper · doi:10.48550/arxiv.1708.00708
In this article, for holomorphic foliations of codimension one at (ℂ3,0), we define the family of second type foliations. This is formed by foliations having, in the reduction process by blow-up maps, only well oriented singularities, meaning that the reduction divisor does not contain weak separatrices of saddle-node singularities. We prove that the reduction of singularities of a non-dicritical foliation of second type coincides with the desingularization of its set of separatrices.