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Projective normality of model varieties and related results


Authors: Paolo Bravi, Jacopo Gandini and Andrea Maffei
Journal: Represent. Theory 20 (2016), 39-93
MSC (2010): Primary 14M27; Secondary 20G05
DOI: https://doi.org/10.1090/ert/477
Published electronically: February 12, 2016
MathSciNet review: 3458949
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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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Additional Information

Paolo Bravi
Affiliation: Dipartimento di Matematica, Sapienza Università di Roma, Piazzale Aldo Moro 5, 00185 Roma, Italy
Email: bravi@mat.uniroma1.it

Jacopo Gandini
Affiliation: Scuola Normale Superiore, Piazza dei Cavalieri 7, 56126 Pisa, Italy
Email: jacopo.gandini@sns.it

Andrea Maffei
Affiliation: Dipartimento di Matematica, Università di Pisa, Largo Bruno Pontecorvo 5, 56127 Pisa, Italy
Email: maffei@dm.unipi.it

DOI: https://doi.org/10.1090/ert/477
Received by editor(s): February 19, 2015
Received by editor(s) in revised form: December 29, 2015
Published electronically: February 12, 2016
Article copyright: © Copyright 2016 American Mathematical Society