Secant varieties and successive minima

2001/10/23 by Soule', Christophe
#14G40 14H99 11H50 11B65 #Algebraic Geometry (math.AG) #FOS: Mathematics #Number Theory (math.NT)

paper · doi:10.48550/arxiv.math/0110254

Abstract

Given an arithmetic surface and a positive hermitian line bundle over it, we bound the successive minima of the lattice of global sections of this line bundle. Our method combines a result of C.Voisin on secant varieties of projective curves with previous work by the author on the arithmetic analog of the Kodaira vanishing theorem. The paper also includes a result of A.Granville on the divisibility properties of binomial coefficients in a given line of Pascal's triangle.

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• Very stable extensions on arithmetic surfaces
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• Successive minima of projective toric varieties