Generic differential equations are strongly minimal

2021/06/04 by Matthew DeVilbiss, James Freitag, DeVilbiss, Matthew +1 · 2 citations
Computer Science · Mathematics · #03C60 #12H05 #Algebraic Geometry (math.AG) #FOS: Mathematics #Functional Equations Stability Results #Logic (math.LO) #Mathematical and Theoretical Analysis #Number Theory (math.NT) #Polynomial and algebraic computation

paper · pdf · doi:10.48550/arxiv.2106.02627

openalex publication_date 2021/06/04 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

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).

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