Email this article Commuting homogeneous locally nilpotent derivations
- Authors: Matveev D.A.1
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Affiliations:
- Faculty of Computer Science, National Research University "Higher School of Economics"
- Issue: Vol 210, No 11 (2019)
- Pages: 103-128
- Section: Articles
- URL: https://ogarev-online.ru/0368-8666/article/view/133301
- DOI: https://doi.org/10.4213/sm9132
- ID: 133301
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Abstract
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.
About the authors
Dmitry Aleksandrovich Matveev
Faculty of Computer Science, National Research University "Higher School of Economics"without scientific degree, no status
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