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March 2010 Linear projections and successive minima
Christophe Soulé
Nagoya Math. J. 197: 45-57 (March 2010). DOI: 10.1215/00277630-2009-002

Abstract

Let X be an arithmetic surface, and let L be a line bundle on X. Choose a metric h on the lattice Λ of sections of L over X. When the degree of the generic fiber of X is large enough, we get lower bounds for the successive minima of (Λ,h) in terms of the normalized height of X. The proof uses an effective version (due to C. Voisin) of a theorem of Segre on linear projections and Morrison's proof that smooth projective curves of high degree are Chow semistable.

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Christophe Soulé. "Linear projections and successive minima." Nagoya Math. J. 197 45 - 57, March 2010. https://doi.org/10.1215/00277630-2009-002

Information

Published: March 2010
First available in Project Euclid: 16 March 2010

zbMATH: 1189.14042
MathSciNet: MR2649279
Digital Object Identifier: 10.1215/00277630-2009-002

Subjects:
Primary: 11H06, 14G40, 14H99

Rights: Copyright © 2010 Editorial Board, Nagoya Mathematical Journal

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Vol.197 • March 2010
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