English

Modules formels locaux de feuilletages holomorphes

Dynamical Systems 2007-05-23 v1 Complex Variables

Abstract

We give a complete list of formal invariants for a large class of formal differential 1-forms \wC[[x,y]]dx+C[[x,y]]dy\w \in \Bbb C [[ x, y]]dx + \Bbb C [[ x, y]]dy. \indent A SL^\hat{SL}-equisingular deformation is an equireducible deformation which leaves invariant both the local formal types and the holonomy representation of the components of the exceptional divisor. We characterize the 1-forms with finite formal type (t.f.f), i.e. those which admit a semi-universal SL^\hat{SL}-equisingular deformation, and we give an explicit combinatorial criterion of finiteness. \indent The set of 1-forms with finite formal type contains a dense open set (in the sense of Krull's topology)in the set of 1-forms of the second kind.

Keywords

Cite

@article{arxiv.math/0402256,
  title  = {Modules formels locaux de feuilletages holomorphes},
  author = {Jean-Francois Mattei and Eliane Salem},
  journal= {arXiv preprint arXiv:math/0402256},
  year   = {2007}
}

Comments

89 pages, french

R2 v1 2026-07-22T17:02:36.183Z