Approximation diophantienne et distribution locale sur une surface torique II
Number Theory
2020-12-23 v2 Algebraic Geometry
Abstract
We propose an empirical formula for the problem of local distribution of rational points of bounded height. This is a local version of the Batyrev-Manin-Peyre principle. We verify this for a toric surface, on which cuspidal rational curves and nodal rational curves all give the best approximations outside a Zariski closed subset. We prove the existence of a limit measure as well as an asymptotic formula for the critical zoom by removing a thin set.
Keywords
Cite
@article{arxiv.1805.03920,
title = {Approximation diophantienne et distribution locale sur une surface torique II},
author = {Zhizhong Huang},
journal= {arXiv preprint arXiv:1805.03920},
year = {2020}
}
Comments
Revised and shortened version.in French. Some material will appear in subsequent work. To appear in Bulletin de la Soci\'et\'e math\'ematique de France. Comments still welcome!