Continuity of volumes on arithmetic varieties
Number Theory
2007-05-23 v2 Algebraic Geometry
Abstract
We introduce the volume function for 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 hermitian invertible sheaf. We also give another several applications, for example, a generalized Hodge index theorem, an arithmetic Bogomolov-Gieseker's inequality, etc.
Cite
@article{arxiv.math/0612269,
title = {Continuity of volumes on arithmetic varieties},
author = {Atsushi Moriwaki},
journal= {arXiv preprint arXiv:math/0612269},
year = {2007}
}
Comments
add applications