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arXiv · 1902.01523

Lie algebras of vertical derivations on semiaffine varieties with torus actions

Ivan Arzhantsev·Alvaro Liendo·Taras Stasyuk
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Abstract

Let X be a normal variety endowed with an algebraic torus action. An additive group action $\alpha$ on X is called vertical if a general orbit of $\alpha$ is contained in the closure of an orbit of the torus action and the image of the torus normalizes the image of $\alpha$ in Aut(X). Our first result in this paper is a classification of vertical additive group actions on X under the assumption that X is proper over an affine variety. Then we establish a criterion as to when the infinitesimal generators of a finite collection of additive group actions on X generate a finite-dimensional Lie algebra inside the Lie algebra of derivations of X.

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Ivan Arzhantsev, Alvaro Liendo, Taras Stasyuk. 2019-02-05. Lie algebras of vertical derivations on semiaffine varieties with torus actions. https://doi.org/10.1016/j.jpaa.2020.106499

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