Secant varieties and successive minima

Author:
Christophe Soulé

Translated by:

Journal:
J. Algebraic Geom. **13** (2004), 323-341

DOI:
https://doi.org/10.1090/S1056-3911-03-00351-5

Published electronically:
December 4, 2003

MathSciNet review:
2047701

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Abstract | References | Additional Information

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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Additional Information

**Christophe Soulé**

Affiliation:
IHES, Le Bois Marie, 35 route de Chartres, F-91440 Bures-sur-Yvette, France

Email:
soule@ihes.fr

DOI:
https://doi.org/10.1090/S1056-3911-03-00351-5

Received by editor(s):
November 20, 2001

Published electronically:
December 4, 2003