Geodesic
Commuting homogeneous locally nilpotent derivations
Sbornik. Mathematics, Tome 210 (2019) no. 11, pp. 1609-1632

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Let $X$ be an affine algebraic variety endowed with an action of complexity one of an algebraic torus $\mathbb T$. It is well known that homogeneous locally nilpotent derivations on the algebra of regular functions $\mathbb K[X]$ can be described in terms of proper polyhedral divisors corresponding to the $\mathbb T$-variety $X$. We prove that homogeneous locally nilpotent derivations commute if and only if a certain combinatorial criterion holds. These results are used to describe actions of unipotent groups of dimension two on affine $\mathbb T$-varieties. Bibliography: 10 titles.
Keywords: $\mathbb T$-variety, graded algebra, locally nilpotent derivation, additive group action. 
@article{SM_2019_210_11_a4,
     author = {D. A. Matveev},
     title = {Commuting homogeneous locally nilpotent derivations},
     journal = {Sbornik. Mathematics},
     pages = {1609--1632},
     publisher = {mathdoc},
     volume = {210},
     number = {11},
     year = {2019},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/SM_2019_210_11_a4/}
}
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D. A. Matveev. Commuting homogeneous locally nilpotent derivations. Sbornik. Mathematics, Tome 210 (2019) no. 11, pp. 1609-1632. http://geodesic.mathdoc.fr/item/SM_2019_210_11_a4/