arXiv:1502.01901 Abstract | arXiv Analytics

arXiv:1502.01901 [math.DS]Abstract References Reviews Resources

On Formal First Integrals for Singularities of Complex Vector Fields

Published 2015-02-06Version 1

We show that, for a generic germ of foliation of dimension one in $(\C^3,0)$, the existence of a formal first integral implies the existence of a holomorphic one. This agrees with the same result in other settings obtained in classic works of Mattei&Moussue and Malgrange. Some properties of formal series and formal first integrals are explored.

Comments: arXiv admin note: text overlap with arXiv:1407.4560 by other authors

Categories: math.DS

Subjects: 37F75, 32S65, 32M25

Keywords: complex vector fields, formal first integral implies, singularities, generic germ, classic works

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