Publications Mathématiques de Besançon
Algèbre et Théorie des Nombres
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Huayi Chen
Sur la comparaison entre les minima et les pentes
(On comparaison between minima and slopes)
Publications mathématiques de Besançon (2018), p. 5-23, doi: 10.5802/pmb.20
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Class. Math.: 14G40, 11H50
Keywords: Hermitian vector bundle, slopes, successive minima

Abstract

One compares the successive minima and successive slopes of a Hermitian vector bundle over an arithmetic curve and establishes a uniform bound for their differences. The proof relies on a general comparison principle of $\mathbb{R}$-filtrations and a link between the geometry of Hermitian vector bundles and the transference problem in geometry of numbers. This result can be applied to study the birational invariants of Hermitian line bundles on an arithmetic projective variety.

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