Effective bound of linear series on arithmetic surfaces
Number Theory
2019-12-19 v2
Abstract
We prove an effective upper bound on the number of effective sections of a hermitian line bundle over an arithmetic surface. It is an effective version of the arithmetic Hilbert--Samuel formula in the nef case. As a consequence, we obtain effective lower bounds on the Faltings height and on the self-intersection of the canonical bundle in terms of the number of singular points on fibers of the arithmetic surface.
Cite
@article{arxiv.1201.2216,
title = {Effective bound of linear series on arithmetic surfaces},
author = {Xinyi Yuan and Tong Zhang},
journal= {arXiv preprint arXiv:1201.2216},
year = {2019}
}