Positive degree and arithmetic bigness

Huayi Chen (1)

1 CMLS - Centre de Mathématiques Laurent Schwartz

We establish, for a generically big Hermitian line bundle, the convergence of truncated Harder-Narasimhan polygons and the uniform continuity of the limit. As an application, we generalize several results of Moriwaki concerning arithmetically big Hermitian line bundles to the case of continuous metrics. Furthermore, we prove a conjecture of him asserting that the arithmetic volume function is actually a limit instead of a sup-limit.

Domaines: Géométrie algébrique [math.AG]; Théorie des nombres [math.NT]

Huayi Chen. Positive degree and arithmetic bigness. 2008. ⟨hal-00264856v1⟩