Projective normality of complete symmetric varieties

2002/06/27 by Rocco Chirivi', Rocco Chirivì, Chirivi', Rocco +2
Mathematics · #14L30 (secondary) #14M17 (Primary) #Advanced Differential Equations and Dynamical Systems #Algebraic Geometry (math.AG) #FOS: Mathematics #Meromorphic and Entire Functions #Representation Theory (math.RT) #Tensor decomposition and applications #math.AG #math.RT #msc:14L30 #msc:14M17

paper · pdf · doi:10.48550/arxiv.math/0206290

Proof for E_7, E_8 in Lemma 4.6 added and minor changes

openalex publication_date 2002/06/27 · arxiv created 2002/10/04 · arxiv updated 2009/11/30 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We prove that in characteristic zero the multiplication of sections of dominant line bundles on a complete symmetric variety X=G/H is a surjective map. As a consequence the cone defined by a complete linear system over X, or over a closed G stable subvariety of X is normal. This gives an affirmative answer to a question raised by Faltings. A crucial point of the proof is a combinatorial property of root systems.

Citations

• The Partial Order of Dominant Weights

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