Open Access
2009 The Geometric Bogomolov Conjecture for Curves of Small Genus
X. W. C. Faber
Experiment. Math. 18(3): 347-367 (2009).


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 $4$ 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.


Download Citation

X. W. C. Faber. "The Geometric Bogomolov Conjecture for Curves of Small Genus." Experiment. Math. 18 (3) 347 - 367, 2009.


Published: 2009
First available in Project Euclid: 25 November 2009

zbMATH: 1186.11035
MathSciNet: MR2555704

Primary: 11G30
Secondary: 11G50 , 14G40

Keywords: Bogomolov conjecture , curves of higher genus , function fields , metric graphs

Rights: Copyright © 2009 A K Peters, Ltd.

Vol.18 • No. 3 • 2009
Back to Top