On Generalised Danielewski Surfaces over fields of arbitrary characteristic

2025/06/02 by Debojyoti Saha, Saha, Debojyoti
Mathematics · #Advanced Harmonic Analysis Research #Advanced Topology and Set Theory #Algebraic Geometry and Number Theory #Commutative Algebra (math.AC) #FOS: Mathematics

paper · pdf · doi:10.48550/arxiv.2506.01457

openalex publication_date 2025/06/02 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

In this paper we study exponential maps (\mathbbG_a-actions) on the family of affine two dimensional surfaces of the form f(x)y=ϕ(x,z) over arbitrary fields, describe the Makar-Limanov invariant and Derksen invariant of these surfaces, give a complete characterization of isomorphisms between such surfaces and display a subfamily which provides counterexamples to the cancellation problem.

Citations

• On Generalised Danielewski and Asanuma varieties
• Isomorphisms between cylinders over Danielewski surfaces
• On the rigidity of small domains

Related

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• On automorphisms of Danielewski surfaces
• Automorphisms of Danielewski varieties
• Danielewski-Fieseler surfaces
• On Generalised Danielewski and Asanuma varieties