Journal of Algebraic Geometry

Journal of Algebraic Geometry

Online ISSN 1534-7486; Print ISSN 1056-3911

   
 
 

 

Uniqueness of embeddings of the affine line into algebraic groups


Authors: Peter Feller and Immanuel van Santen
Journal: J. Algebraic Geom. 28 (2019), 649-698
DOI: https://doi.org/10.1090/jag/725
Published electronically: May 31, 2019
MathSciNet review: 3994309
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Abstract | References | Additional Information

Abstract: Let $ Y$ be the underlying variety of a complex connected affine algebraic group. We prove that two embeddings of the affine line $ \mathbb{C}$ into $ Y$ are the same up to an automorphism of $ Y$ provided that $ Y$ is not isomorphic to a product of a torus $ (\mathbb{C}^\ast )^k$ and one of the three varieties $ \mathbb{C}^3$, $ \operatorname {SL}_2$, and  $ \operatorname {PSL}_2$.


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Peter Feller
Affiliation: Department of Mathematics, ETH Zürich, Rämistr. 101, 8092 Zürich, Switzerland
Email: peter.feller@math.ch

Immanuel van Santen
Affiliation: Fachbereich Mathematik, Universität Hamburg, Bundesstr. 55, 20146 Hamburg, Germany
Email: immanuel.van.santen@math.ch

DOI: https://doi.org/10.1090/jag/725
Received by editor(s): September 10, 2017
Received by editor(s) in revised form: March 30, 2018, and April 16, 2018
Published electronically: May 31, 2019
Article copyright: © Copyright 2019 University Press, Inc.