On Generalised Danielewski Surfaces over fields of arbitrary characteristic

Debojyoti Saha

On Generalised Danielewski Surfaces over fields of arbitrary characteristic

Commutative Algebra 2025-06-03 v1

Authors: Debojyoti Saha

Abstract

In this paper we study exponential maps ( $\mathbb{G}_a$ -actions) on the family of affine two dimensional surfaces of the form $f(x)y=\phi(x,z)$ 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.

Keywords

Danielewski surface exponential map Makar-Limanov invariant Derksen invariant cancellation problem affine surface

Cite

@article{arxiv.2506.01457,
  title  = {On Generalised Danielewski Surfaces over fields of arbitrary characteristic},
  author = {Debojyoti Saha},
  journal= {arXiv preprint arXiv:2506.01457},
  year   = {2025}
}

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