Desingularization of three-dimensional vector field having a meromorphic first integral
by
Daniel Panazzolo
Universidade de Sao Paulo
Coauthors: Felipe Cano (Universidad de Valladolid)

The desingularization of vector fields and, more generally, of differential systems of arbitrary order is still a problem which is widely open. In short, there is the well-known Bendixson-Seidenberg's result on the desingularization of vector fields/1-forms in dimension two, and the results of F.Cano on desingularization of 1-forms in dimension three. Besides that, Cano has proven a "local" version of a desingularization theorem for three-dimensional vector fields (see Lect. Notes in Math. 1259). In this talk, we will describe a general desingularization theorem for three-dimensional vector fields which have a meromorphic first integral. In particular, this includes the category of all 1-parameter families of two-dimensional vector field and partially proves a conjecture of Denkowska and Roussarie.

Date received: May 31, 1999

Copyright © 1999 by the author(s). The author(s) of this document and the organizers of the conference have granted their consent to include this abstract in Atlas Conferences Inc. Document # cacv-56.