Integral points of bounded height on a certain toric variety

We determine an asymptotic formula for the number of integral points of bounded height on a certain toric variety, which is incompatible with part of a preprint by Chambert-Loir and Tschinkel. We provide an alternative interpretation of the asymptotic formula we get. To do so, we construct an analogue of Peyre’s constant α<!-- α --> α and describe its relation to a new obstruction to the Zariski density of integral points in certain regions of varieties.