The Geometric Bogomolov Conjecture for Small Genus Curves
Number Theory
2009-07-13 v3 Algebraic Geometry
Abstract
The Bogomolov Conjecture is a finiteness statement about algebraic points of small height on a smooth complete curve defined over a global field. We verify an effective form of the Bogomolov Conjecture for all curves of genus at most 4 defined over a function field of characteristic zero. We recover the known result for genus 2 curves and in many cases improve upon the known bound for genus 3 curves. For many curves of genus 4 with bad reduction, the conjecture was previously unproved.
Cite
@article{arxiv.0803.0855,
title = {The Geometric Bogomolov Conjecture for Small Genus Curves},
author = {X. W. C. Faber},
journal= {arXiv preprint arXiv:0803.0855},
year = {2009}
}
Comments
47 pages total (31 pages in body of article, 8 pages of Mathematica code, 8 pages of Mathematica notebooks); ramification typo corrected in formulas on pp.13-14, this is the final version