The Valuative Theory of Foliations
arXiv:math/0103123
Abstract
We describe the valuations following infinitely near singular points of a (singular) holomorphic foliation in the complex plane. They appear to be those satisfying a generalization of L'Hopital's rule. With them, we characterize dicritical vector fields, generic simple singularities, the existence of non- convergent solutions, etc. The construction is generalizable to dimension n.
16 pages, uses package: diagram.tex