Positive degree and arithmetic bigness

Details Positive degree and arithmetic bigness Positive degree and arithmetic bigness

2008-03-18

arxiv.org/abs/0803.2583v3

Mathematics

Algebraic Geometry

Scientific paper

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.

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