Archiv der Mathematik

, Volume 108, Issue 1, pp 17–27 | Cite as

The Cox ring of a complexity-one horospherical variety

  • Kevin Langlois
  • Ronan TerpereauEmail author
Open Access


Cox rings are intrinsic objects naturally generalizing homogeneous coordinate rings of projective spaces. A complexity-one horospherical variety is a normal variety equipped with a reductive group action whose general orbit is horospherical and of codimension one. In this note, we provide a presentation by generators and relations for the Cox rings of complete rational complexity-one horospherical varieties.


Action of algebraic groups Luna–Vust theory 

Mathematics Subject Classification

14L30 14M27 14M25 


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© The Author(s) 2017

Open AccessThis article is distributed under the terms of the Creative Commons Attribution 4.0 International License (, which permits unrestricted use, distribution, and reproduction in any medium, provided you give appropriate credit to the original author(s) and the source, provide a link to the Creative Commons license, and indicate if changes were made.

Authors and Affiliations

  1. 1.Mathematisches Institut, Heinrich Heine UniversitätDüsseldorfGermany
  2. 2.Max Planck Institut für MathematikBonnGermany

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