Characteristic curves of holomorphic foliations
Rudy Rosas
Journal of Singularities
volume 26 (2023), 76-91
Received: 13 June 2023. Received in revised form: 20 October 2023.
Abstract:
Let F be a germ of holomorphic foliation with an isolated singularity at 0 in C^2 A characteristic curve of F is a continuous one-dimensional curve tending to 0 in C^2, tangent to F and having some "tame" oscillating behavior, which is a kind of generalization of a separatrix. We define a notion of resolution of the set of characteristic curves of F and show that this process gives another way of obtaining the resolution of singularities of the foliation.
Author(s) information:
Rudy Rosas
Pontificia Universidad Católica del Perú
Av. Universitaria 1801
Lima, Peru
email: rudy.rosas@pucp.edu.pe