Projective normality of model varieties and related results

Abstract

We prove that the multiplication of sections of globally generated line bundles on a model wonderful variety M of simply connected type is always surjective. This follows by a general argument which works for every wonderful variety and reduces the study of the surjectivity for every couple of globally generated line bundles to a finite number of cases. As a consequence, the cone defined by a complete linear system over M or over a closed G-stable subvariety of M is normal. We apply these results to the study of the normality of the compactifications of model varieties in simple projective spaces and of the closures of the spherical nilpotent orbits. Then we focus on a particular case proving two specific conjectures of Adams, Huang and Vogan on an analogue of the model orbit of the group of type E8.

v2: 54 pages, new introduction and several minor changes, added Proposition 9.2. To appear on Representation Theory

References in corpus (3)

• An introduction to wonderful varieties with many examples of type F4
• Spherical orbit closures in simple projective spaces and their normalizations
• Normality and non-normality of group compactifications in simple projective spaces

Cited by in corpus (4)

• Regular functions on spherical nilpotent orbits in complex symmetric pairs: classical non-Hermitian cases
• Standard monomial theory for wonderful varieties
• Regular functions on spherical nilpotent orbits in complex symmetric pairs: classical Hermitian cases
• Pl\:ucker relations and spherical varieties: application to model varieties