The Cox ring of a complexity-one horospherical variety

Kevin Langlois (1) , Ronan Terpereau (2)

1 Mathematisches Institut [Dusseldorf]
2 MPI - Max-Planck-Institut für Mathematik

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.

Mots clés: Luna-Vust theory; Action of algebraic groups

Domaines: Géométrie algébrique [math.AG]

Kevin Langlois, Ronan Terpereau. The Cox ring of a complexity-one horospherical variety. Archiv der Mathematik, 2017, 108 (1), pp.17-27. ⟨10.1007/s00013-016-0979-y⟩. ⟨hal-01421938⟩