Isotropy subgroups of homogeneous locally nilpotent derivations

TL;DR

This paper characterizes isotropy groups of maximal homogeneous locally nilpotent derivations on affine toric varieties and trinomial hypersurfaces, providing criteria for maximality.

Contribution

It offers a description of isotropy groups and criteria for maximality of homogeneous locally nilpotent derivations on specific algebraic varieties.

Findings

Describes isotropy groups of maximal homogeneous locally nilpotent derivations.

Provides criteria for maximality of these derivations on affine toric varieties and trinomial hypersurfaces.

Abstract

We say that a locally nilpotent derivations $\delta$ is maximal if there are no inequivalent locally nilpotent derivations that commute with $\delta$. The paper gives a description of isotropy groups of maximal homogeneous locally nilpotent derivations on affine toric varieties and on certain trinomial hypersurfaces. Moreover, the criteria for homogeneous locally nilpotent derivations to be maximal were obtained for these classes of varieties.