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Positive degree and arithmetic bigness
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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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Adelic Line Bundles, Arithmetic Positivity and Diophantine Geometry
Expository account of adelic line bundles, arithmetic positivity, and applications to equidistribution and uniform Bogomolov conjecture.
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