English

The Valuative Theory of Foliations

Algebraic Geometry 2007-05-23 v1 Commutative Algebra

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.

Keywords

Cite

@article{arxiv.math/0103123,
  title  = {The Valuative Theory of Foliations},
  author = {Pedro Fortuny Ayuso},
  journal= {arXiv preprint arXiv:math/0103123},
  year   = {2007}
}

Comments

16 pages, uses package: diagram.tex

R2 v1 2026-07-22T16:37:46.619Z