Horospherical two-orbit varieties as zero loci
Résumé
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.
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