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 / Chirivi, R; Maffei, Andrea. - In: DUKE MATHEMATICAL JOURNAL. - ISSN 0012-7094. - 122:(2004), pp. 93-123. [10.1215/S0012-7094-04-12213-4]
Projective normality of complete symmetric varieties
MAFFEI, Andrea
2004
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 allegati a questo prodotto
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