Hyperbola method on toric varieties

Abstract

We develop a very general version of the hyperbola method which extends the known method by Blomer and Brüdern for products of projective spaces to a very large class of toric varieties. We use it to count Campana points of bounded log-anticanonical height on many split toric Q-varieties with torus invariant boundary. We apply the strong duality principle in linear programming to show the compatibility of our results with the conjectured asymptotic.