In this article we study Diophantine approximation and local distribution of a rational point 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 a quadratic point on the projective line.
Categories: math.NT