English

Topological Moduli Space for Germs of Holomorphic Foliations III: Complete families

Dynamical Systems 2024-06-07 v2 Classical Analysis and ODEs Complex Variables

Abstract

In this work we use our previous results on the topological classification of generic singular foliation germs on (C2,0)(\mathbb C^{2},0) to construct complete families: after fixing the semi-local topological invariants we prove the existence of a minimal family of foliation germs that contain all the topological classes and such that any equisingular global family with parameter space an arbitrary complex manifold factorizes through it.

Keywords

Cite

@article{arxiv.2201.07479,
  title  = {Topological Moduli Space for Germs of Holomorphic Foliations III: Complete families},
  author = {David Marín and Jean-François Mattei and Eliane Salem},
  journal= {arXiv preprint arXiv:2201.07479},
  year   = {2024}
}

Comments

The paper entitled "Topologically complete families of germs of holomorphic foliations" with reference arXiv:2105.12688 (version 1) has been modified and divided in two parts: the paper "Topological moduli space for germs of holomorphic foliations II: Universal deformations" with reference arXiv:2105.12688v2 and the current paper