Projective normality of model varieties and related results

Bravi, Paolo; Gandini, Jacopo; Maffei, Andrea

doi:10.1090/ert/477

Projective normality of model varieties and related results
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by Paolo Bravi, Jacopo Gandini and Andrea Maffei

Represent. Theory 20 (2016), 39-93

DOI: https://doi.org/10.1090/ert/477

Published electronically: February 12, 2016

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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 $\mathsf E_8$.

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