Horospherical two-orbit varieties as zero loci

Abstract

We present geometric realizations of horospherical two-orbit varieties, by showing that their blow-up along the unique closed invariant orbit is the zero locus of a general section of a homogeneous vector bundle over some auxiliary variety. As an application, we compute the cohomology ring of the G 2 G_2 -variety, including its quantum version. We also consider the S p i n 7 Spin_7 -variety, which deserves a different treatment.