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arXiv · 1706.08572

Analytic Moduli of Plane Branches and Holomorphic Flows

Pedro Fortuny Ayuso·Javier Ribón
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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 $({\mathbb C}^{2},0)$. 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.

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Pedro Fortuny Ayuso, Javier Ribón. 2018-06-05. Analytic Moduli of Plane Branches and Holomorphic Flows. https://doi.org/10.4153/s0008414x19000221

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