On Generalised Danielewski Surfaces over fields of arbitrary characteristic

Debojyoti Saha

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arXiv · 2506.01457

On Generalised Danielewski Surfaces over fields of arbitrary characteristic

Debojyoti Saha

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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.

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Debojyoti Saha. 2025-06-02. On Generalised Danielewski Surfaces over fields of arbitrary characteristic. https://arxiv.org/abs/2506.01457

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