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Linear projections and successive minima

Published online by Cambridge University Press:  11 January 2016

Christophe Soulé
Christophe Soulé*
Affiliation:
Institut des Hautes Études Scientifiques, 35 Route de Chartres, 91440 Bures-sur-Yvette, Francesoule@ihes.fr
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Abstract

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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.

Keywords

14H9914G4011H06
Type
Research Article
Information
Nagoya Mathematical Journal , Volume 197 , March 2010 , pp. 45 - 57
Copyright
Copyright © Editorial Board of Nagoya Mathematical Journal 2010

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