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arXiv · 0902.2868

Existence of non-algebraic singularities of differential equation

Yohann Genzmer·Loïc Teyssier
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Abstract

An algebraizable singularity is a germ of a singular holomorphic foliation which can be defined in some appropriate local chart by a differential equation with algebraic coefficients. We show that there exists at least countably many saddle-node singularities of the complex plane that are not algebraizable.

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Yohann Genzmer, Loïc Teyssier. 2009-02-17. Existence of non-algebraic singularities of differential equation. https://doi.org/10.1016/j.jde.2009.10.001

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