The freeness property for locally nilpotent derivations of k[x,y,z]

2020/09/30 by Daniel Daigle, Daigle, Daniel
Mathematics · #14R20 #Advanced Differential Equations and Dynamical Systems #Algebraic Geometry (math.AG) #Algebraic Geometry and Number Theory #Commutative Algebra (math.AC) #FOS: Mathematics #Meromorphic and Entire Functions #Primary: 13N15 Secondary: 14R10

paper · pdf · doi:10.48550/arxiv.2009.14800

openalex publication_date 2020/09/30 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We prove Freudenburg's Freeness Conjecture: Let B be the polynomial ring in three variables over a field of characteristic zero, let D : B --> B be a nonzero locally nilpotent derivation, and let A = ker(D). Then B is a free A-module, and there exists a basis (e_i)_{i ∈ ℕ} of B such that deg_D(e_i) = i for all i ∈ ℕ.

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