The Valuative Theory of Foliations

Details The Valuative Theory of Foliations The Valuative Theory of Foliations

2001-03-20

arxiv.org/abs/math/0103123v1

Mathematics

Algebraic Geometry

16 pages, uses package: diagram.tex

Scientific paper

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.

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