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Secant varieties and successive minima

Christophe Soule'
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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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Christophe Soule'. 2001-10-23. Secant varieties and successive minima. https://arxiv.org/abs/math/0110254

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