Approximation diophantienne et distribution locale sur une surface torique
Volume 189 / 2019
Acta Arithmetica 189 (2019), 1-94
MSC: Primary 11G50, 11K60, 14M25.
DOI: 10.4064/aa170327-4-1
Published online: 26 April 2019
Abstract
We study Diophantine approximation and local distribution of rational points on a toric surface obtained as a blow-up of $\mathbb{P}^1\times\mathbb{P}^1$. It turns out that outside a Zariski closed subset the best approximations are achieved through a family of nodal curves. Hence the investigation is reduced to the question of local distribution of quadratic points on the projective line.
