Inequalities for semistable families of arithmetic varieties
alg-geom
2007-05-23 v3 Algebraic Geometry
Abstract
In this paper, we will consider a generalization of Bogomolov's inequality and Cornalba-Harris-Bost's inequality to semistable families of arithmetic varieties under the idea that geometric semistability implies a certain kind of arithmetic positivity. The first one is an arithmetic analogue of the relative Bogomolov's inequality proved by the second author. We also establish the arithmetic Riemann-Roch formulae for stable curves over regular arithmetic varieties and generically finite morphisms of arithmetic varieties.
Keywords
Cite
@article{arxiv.alg-geom/9710007,
title = {Inequalities for semistable families of arithmetic varieties},
author = {Shu Kawaguchi and Atsushi Moriwaki},
journal= {arXiv preprint arXiv:alg-geom/9710007},
year = {2007}
}
Comments
Version 3.0 (75 pages), the new version of the paper titled "Relative Bogomolov's inequality in the arithmetic case"