Projective normality of complete symmetric varieties

Details Projective normality of complete symmetric varieties Projective normality of complete symmetric varieties

2002-06-27

arxiv.org/abs/math/0206290v2

Mathematics

Algebraic Geometry

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

Scientific paper

We prove that in characteristic zero the multiplication of sections of dominant line bundles on a complete symmetric variety $X=\bar{G/H}$ 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.

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