Semisimple derivations, rational slice and kernels over affine domains
Algebraic Geometry
2026-03-23 v1
Abstract
Let k be an algebraically closed field of characteristic zero and let B be a finitely generated k-domain. We study semisimple derivations on B, with special emphasis on those whose eigenvalues are integers. For such derivations, after passing to the field of fractions and choosing a rational slice s with D(s) = s, we describe the kernel of D explicitly in terms of semi-invariant generators. We also obtain descriptions of the kernel on suitable localizations of B and on B itself by intersection. Several basic properties of semisimple derivations and their behavior under conjugation are also discussed
Cite
@article{arxiv.2603.19587,
title = {Semisimple derivations, rational slice and kernels over affine domains},
author = {Luis Cid},
journal= {arXiv preprint arXiv:2603.19587},
year = {2026}
}