Existence of non-algebraic singularities of differential equation
arXiv:0902.2868 · doi:10.1016/j.jde.2009.10.001
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.
11 pages