Positive degree and arithmetic bigness

2008/03/18 by Huayi Chen, Chen, Huayi
Mathematics · #Algebraic Geometry (math.AG) #FOS: Mathematics #Number Theory (math.NT) #math.AG #math.NT

paper · pdf · doi:10.48550/arxiv.0803.2583

arxiv created 2008/05/04 · arxiv updated 2009/12/01

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.

Related

• Convergence of Harder-Narasimhan polygons
• Harder-Narasimhan polygons and Laws of Large Numbers
• On Volumes of Arithmetic Line Bundles II
• Volumes of Arithmetic Okounkov Bodies
• On the Irreducibility and Distribution of Arithmetic Divisors