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arXiv · 1506.00164

Locally nilpotent derivations and automorphism groups of certain Danielewski surfaces

Angelo Calil Bianchi·Marcelo Oliveira Veloso
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Abstract

We describe the set of all locally nilpotent derivations of the quotient ring $\mathbb{K}[X,Y,Z]/(f(X)Y - φ(X,Z))$ constructed from the defining equation $f(X)Y = φ(X,Z)$ of a generalized Danielewski surface in $\mathbb K^3$ for a specific choice of polynomials $f$ and $φ$, with $\mathbb K$ an algebraically closed field of characteristic zero. As a consequence of this description we calculate the $ML$-invariant and the Derksen invariant of this ring. We also determine a set of generators for the group of $\mathbb K$-automorphisms of $\mathbb K[X,Y,Z]/(f(X)Y - φ(Z))$ also for a specific choice of polynomials $f$ and $φ$.

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BibTeXRIS

Angelo Calil Bianchi, Marcelo Oliveira Veloso. 2015-05-30. Locally nilpotent derivations and automorphism groups of certain Danielewski surfaces. https://doi.org/10.1016/j.jalgebra.2016.08.030

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