Horospherical two-orbit varieties as zero loci

Boris Pasquier (1) , Laurent Manivel (2)

1 LMA [Poitiers] - Laboratoire de mathématiques et applications [UMR 7348]
2 IMT - Institut de Mathématiques de Toulouse UMR5219

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-variety, including its quantum version. We also consider the Spin_7-variety, which deserves a different treatment.

Mots clés: Fano variety; horospherical variety; exceptional Lie group; blow-up; vector bundle; Chow ring; quantum cohomology

Domaines: Géométrie algébrique [math.AG]

Boris Pasquier, Laurent Manivel. Horospherical two-orbit varieties as zero loci. 2020. ⟨hal-03048217⟩