Gap for geometric canonical height functions
Algebraic Geometry
2024-04-15 v2 Dynamical Systems
Abstract
We prove the existence of a gap around zero for canonical height functions associated to endomorphisms of projective spaces defined over complex function fields. We also prove that if the rational points of height zero are Zariski dense, then the endomorphism is birationally isotrivial. As a corollary, by a result of S. Cantat and J. Xie, we have a geometric Northcott property on projective plane in the same spirit of results of R. Benedetto, M. Baker and L. Demarco on the projective line.
Keywords
Cite
@article{arxiv.2307.08561,
title = {Gap for geometric canonical height functions},
author = {Yugang Zhang},
journal= {arXiv preprint arXiv:2307.08561},
year = {2024}
}
Comments
Final version