The automorphism theorem and additive group actions on the affine plane

2016/04/14 by Shigeru Kuroda, Kuroda, Shigeru
Mathematics · #14R20 #Advanced Algebra and Geometry #Advanced Differential Equations and Dynamical Systems #Advanced Topics in Algebra #Algebraic Geometry (math.AG) #Commutative Algebra (math.AC) #FOS: Mathematics #Primary 14R10 #Secondary 13A50

paper · pdf · doi:10.48550/arxiv.1604.04070

openalex publication_date 2016/04/14 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

Due to Rentschler, Miyanishi and Kojima, the invariant ring for a \bf G_a-action on the affine plane over an arbitrary field is generated by one coordinate. In this note, we give a new short proof for this result using the automorphism theorem of Jung and van der Kulk.

Related

• Invariant Rings and Quasiaffine Quotients
• Separating invariants for arbitrary linear actions of the additive group
• Computing invariants of algebraic group actions in arbitrary characteristic
• Reductive and unipotent actions of affine groups
• On algebraic spaces with an action of G_m