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Lines in affine toric varieties

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Abstract

We prove that up to automorphisms of the target the affine line \({\mathbb{A}^1}\) admits a unique embedding into the regular part of an affine simplicial toric variety of dimension at least 4 which is smooth in codimension 2. This is an analog of the well-known result on the existence of a linearization of any polynomial embedding \({\mathbb{A}^1}\hookrightarrow{\mathbb{A}^n}\) for n ≥ 1.

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Acknowlegement

The author is grateful to the referee for very useful comments and corrections.

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  1. Department of Mathematics, University of Miami, Coral Gables, FL, 33124, USA

    Shulim Kaliman

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  1. Shulim Kaliman
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Correspondence to Shulim Kaliman.

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Kaliman, S. Lines in affine toric varieties. Isr. J. Math. 250, 85–113 (2022). https://doi.org/10.1007/s11856-022-2332-4

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  • DOI: https://doi.org/10.1007/s11856-022-2332-4

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