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arXiv · 2208.11755

On the automorphism group of non-necessarily normal affine toric varieties

Roberto Díaz·Alvaro Liendo
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Abstract

Our main result is the following: let X be a normal affine toric surface without torus factor. Then there exists a non-normal affine toric surface X' with automorphism group isomorphic to the automorphism group of X if and only if X is different from the affine plane. As a tool, we first provide a classification of normalized additive group actions on a non-necessarily normal affine toric variety X of any dimension. Recall that normalized additive group actions on X are in correspondence with homogeneous locally nilpotent derivations on the algebra of regular functions of X. More generally, we provide a classification of homogeneous locally nilpotent derivations on the semigroup algebra of a commutative cancellative monoid.

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Roberto Díaz, Alvaro Liendo. 2022-08-24. On the automorphism group of non-necessarily normal affine toric varieties. https://doi.org/10.1093/imrn%2Frnad050

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