We prove that in characteristic zero the multiplication of sections of line bundles generated by global sections 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 in [11]. A crucial point of the proof is a combinatorial property of root systems.

Protective normality of complete symmetric varieties

Chirivi' Rocco;
2004

Abstract

We prove that in characteristic zero the multiplication of sections of line bundles generated by global sections 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 in [11]. A crucial point of the proof is a combinatorial property of root systems.
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Utilizza questo identificativo per citare o creare un link a questo documento: http://hdl.handle.net/11587/467685
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