The Cox ring of a complexity-one horospherical variety
  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. 
Kevin Langlois, Ronan Terpereau
math.AG math.RT