Duke Mathematical Journal

Projective normality of complete symmetric varieties

Rocco Chirivì and Andrea Maffei

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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.

Article information

Duke Math. J., Volume 122, Number 1 (2004), 93-123.

First available in Project Euclid: 24 March 2004

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Mathematical Reviews number (MathSciNet)

Zentralblatt MATH identifier

Primary: 14M17: Homogeneous spaces and generalizations [See also 32M10, 53C30, 57T15]
Secondary: 14L30: Group actions on varieties or schemes (quotients) [See also 13A50, 14L24, 14M17]


Chirivì, Rocco; Maffei, Andrea. Projective normality of complete symmetric varieties. Duke Math. J. 122 (2004), no. 1, 93--123. doi:10.1215/S0012-7094-04-12213-4. https://projecteuclid.org/euclid.dmj/1080137203

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