Institute for Mathematical Sciences

Preprint ims02-03

J. C. Rebelo
Complete polynomial vector fields on $\C^2$,{\sc Part I}

Abstract: 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 [Fo].
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