arXiv subjects
Publications and source records attributed to Julio C. Rebelo.
These are slightly informal lecture notes intended for graduate students about the standard local theory of holomorphic foliations and vector fields. Though the material presented here is well-known some of the proofs differs slightly from the classical arguments.
In this work, under a mild assumption, we give the classification of the complete polynomial vector fields in two variables up to algebraic automorphisms of $\C^2$. The general problem is also reduced to the study of the combinatorics of certain resolutions of singularities. Whereas we deal with $\C$-complete vector fields, our results also apply to $\R$-complete ones thanks to a theorem of Forstneric \cite{forst}.