Approximation diophantienne et distribution locale sur une surface torique II
arXiv:1805.03920 · doi:10.24033/bsmf.2803
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.
Revised and shortened version.in French. Some material will appear in subsequent work. To appear in Bulletin de la Société mathématique de France. Comments still welcome!