Positive degree and arithmetic bigness

Abstract

We establish, for a generically big Hermitian line bundle, the convergence of truncated Harder-Narasimhan polygons and the uniform continuity of the limit. As applications, we prove a conjecture of Moriwaki asserting that the arithmetic volume function is actually a limit instead of a sup-limit, and we show how to compute the asymptotic polygon of a Hermitian line bundle, by using the arithmetic volume function.

References in corpus (2)

• Hermitian vector bundles and extension groups on arithmetic schemes. II. The arithmetic Atiyah extension
• Continuity of volumes on arithmetic varieties

Cited by in corpus (12)

• Differentiability of non-archimedean volumes and non-archimedean Monge-Ampère equations (with an appendix by Robert Lazarsfeld)
• Estimation of arithmetic linear series
• Big arithmetic divisors on the projective spaces over Z
• Effective bound of linear series on arithmetic surfaces
• Roth's Theorem over arithmetic function fields
• Non-Archimedean volumes of metrized nef line bundles
• Adelic divisors on arithmetic varieties
• Zariski decompositions on arithmetic surfaces
• Majorations explicites de fonctions de Hilbert-Samuel géométrique et arithmétique
• Continuous extension of arithmetic volumes
• Volumes of Arithmetic Okounkov Bodies
• Higher dimensional essential minima and equidistribution of cycles