Integral points of bounded height on a log Fano threefold

Abstract

We determine an asymptotic formula for the number of integral points of bounded height on a blow-up of P 3 outside certain planes using universal torsors.

Integral points on singular del Pezzo surfaces

“…In [Wil21a], it behaves similarly as Peyre's α for projective varieties since the boundary has just one component; it is also much simpler since the Picard number is 2. Our second and following cases behave in a different way since the Clemens complex is not a simplex, providing the first nontrivial treatment of this factor for a nontoric variety.…”

“…Therefore, we adapt the universal torsor method to integral points in order to confirm new cases of an integral analogue of Manin's conjecture. See also [Wil21a] for a three-dimensional example.…”