On the algebraicity of germs of meromorphic functions

In this article we prove that every germ of analytic meromorphic function at $(\mathbb{C}^{2},0)$ is equivalent, under the right composition by a germ of biholomorphism, to a germ of algebraic meromorphic function. An analogous result is also true for real analytic meromorphic functions.

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Bibliographic Details
Main Authors Genzmer, Yohann, Mol, Rogério
Format Journal Article
LanguageEnglish
Published 24.02.2023
Subjects
Mathematics - Complex Variables
Mathematics - Dynamical Systems
Online AccessGet full text
DOI10.48550/arxiv.2302.12860

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Summary:In this article we prove that every germ of analytic meromorphic function at $(\mathbb{C}^{2},0)$ is equivalent, under the right composition by a germ of biholomorphism, to a germ of algebraic meromorphic function. An analogous result is also true for real analytic meromorphic functions.
DOI:10.48550/arxiv.2302.12860