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arXiv · 2603.19587

Semisimple derivations, rational slice and kernels over affine domains

Luis Cid
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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

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Luis Cid. 2026-03-20. Semisimple derivations, rational slice and kernels over affine domains. https://arxiv.org/abs/2603.19587

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