arXiv subjects

Eliane Salem

Publications and source records attributed to Eliane Salem.

3 recordsLinked to original sources

arXiv2024

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

In this work we use our previous results on the topological classification of generic singular foliation germs on $(\mathbb C^{2},0)$ 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.

math.DS↗

arXiv2023

Topology of singular foliation germs in $\mathbb C^2$

The object of this survey is to give an overview on the topology of singularities of holomorphic foliation germs on $(\mathbb C^2,0)$.

math.CV↗

arXiv2004

Modules formels locaux de feuilletages holomorphes

We give a complete list of formal invariants for a large class of formal differential 1-forms $\w \in \Bbb C [[ x, y]]dx + \Bbb C [[ x, y]]dy$. \indent A $\hat{SL}$-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 $\hat{SL}$-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.

math.DS↗