Nagoya Mathematical Journal

Linear projections and successive minima

Christophe Soulé

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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.

Article information

Source
Nagoya Math. J., Volume 197 (2010), 45-57.

Dates
First available in Project Euclid: 16 March 2010

Permanent link to this document
https://projecteuclid.org/euclid.nmj/1268749075

Digital Object Identifier
doi:10.1215/00277630-2009-002

Mathematical Reviews number (MathSciNet)
MR2649279

Zentralblatt MATH identifier
1189.14042

Subjects
Primary: 14H99: None of the above, but in this section 14G40: Arithmetic varieties and schemes; Arakelov theory; heights [See also 11G50, 37P30] 11H06: Lattices and convex bodies [See also 11P21, 52C05, 52C07]

Citation

Soulé, Christophe. Linear projections and successive minima. Nagoya Math. J. 197 (2010), 45--57. doi:10.1215/00277630-2009-002. https://projecteuclid.org/euclid.nmj/1268749075


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