Analytic Moduli of Plane Branches and Holomorphic Flows
Abstract
We study the behaviour (in the infinitesimal neighbourhood of the singularity) of a singular plane branch under the action of holomorphic flows. The techniques we develop provide a new elementary, geometric and dynamical solution to Zariski's moduli problem for singular branches in . Furthermore, we study whether elements of the same class of analytic conjugacy are conjugated by a holomorphic flow; in particular we show that there exists an analytic class that is not complete: meaning that there are two elements of the class that are not analytically conjugated by a local diffeomorphism embedded in a one-parameter flow.
Cite
@article{arxiv.1706.08572,
title = {Analytic Moduli of Plane Branches and Holomorphic Flows},
author = {Pedro Fortuny Ayuso and Javier Ribón},
journal= {arXiv preprint arXiv:1706.08572},
year = {2022}
}
Comments
This version supersedes the previous one: the title has changed as a consequence of major improvements and new results. This work must be considered a joint work of both authors from now on