Journal of Algebraic Geometry

Author(s): Atsushi Moriwaki
Journal: J. Algebraic Geom.
Posted: May 13, 2008
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Abstract: We introduce the volume function for $C^{\infty}$ -hermitian invertible sheaves on an arithmetic variety as an analogue of the geometric volume function. The main result of this paper is the continuity of the arithmetic volume function. As a consequence, we have the arithmetic Hilbert-Samuel formula for a nef $C^{\infty}$ -hermitian invertible sheaf. We also give other applications, for example, a generalized Hodge index theorem, an arithmetic Bogomolov-Gieseker's inequality, etc.

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