Positive degree and arithmetic bigness

Huayi Chen (1, 2)

1 CMLS - Centre de Mathématiques Laurent Schwartz
2 IHES - Institut des Hautes Études Scientifiques

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.

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

Huayi Chen. Positive degree and arithmetic bigness. 2008. ⟨hal-00264856v4⟩