Generic differential equations are strongly minimal

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 $h$ differential equations with nonconstant coefficients are strongly minimal, answering a question of Poizat (1980).

26 pages. Minor changes and reorganization. To appear in Compositio Mathematica

Cited by in corpus (1)

• On the density of strongly minimal algebraic vector fields