Abstract
We show that any normal irreducible affine n-dimensional SLn-variety X is determined by its automorphism group seen as an ind-group in the category of normal irreducible affine varieties. In other words, if Y is an irreducible affine normal algebraic variety such that Aut(Y) ≃ Aut(X) as an ind-group, then Y ≃ X as a variety. If we drop the condition of normality on Y , then this statement fails. In case n ≥ 3, the result above holds true if we replace Aut(X) by 𝒰(X), where 𝒰(X) is the subgroup of Aut(X) generated by all one-dimensional unipotent subgroups. In dimension 2 we have some interesting exceptions.
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Andriy Regeta is supported by SNF (Schweizerischer Nationalfonds), project number P2BSP2 165390.
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REGETA, A. CHARACTERIZATION OF n-DIMENSIONAL NORMAL AFFINE SLn-VARIETIES. Transformation Groups 27, 271–293 (2022). https://doi.org/10.1007/s00031-022-09701-3
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DOI: https://doi.org/10.1007/s00031-022-09701-3