We prove that in characteristic zero the multiplication of sections of dominant line bundles on a complete symmetric variety X=\overline{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 in [F]. A crucial point of the proof is a combinatorial property of root systems.
Projective normality of complete symmetric varieties
MAFFEI, ANDREA
2004-01-01
Abstract
We prove that in characteristic zero the multiplication of sections of dominant line bundles on a complete symmetric variety X=\overline{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 in [F]. A crucial point of the proof is a combinatorial property of root systems.File in questo prodotto:
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