Generic differential equations are strongly minimal
Logic
2023-02-10 v3 Algebraic Geometry
Number Theory
Abstract
In this manuscript we develop a new technique for showing that a nonlinear algebraic differential equation is strongly minimal based on the recently developed notion of the degree of nonminimality of Freitag and Moosa. Our techniques are sufficient to show that generic order differential equations with nonconstant coefficients are strongly minimal, answering a question of Poizat (1980).
Keywords
Cite
@article{arxiv.2106.02627,
title = {Generic differential equations are strongly minimal},
author = {Matthew DeVilbiss and James Freitag},
journal= {arXiv preprint arXiv:2106.02627},
year = {2023}
}
Comments
26 pages. Minor changes and reorganization. To appear in Compositio Mathematica