On Galois descent of complete intersections

We introduce a notion of strict complete intersections with respect to Cox rings and we prove Galois descent for this new notion.Comment: 8 pages; minor revisio

Torsors and generalized Cox rings for Manin's conjecture

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Hyperbola method on toric varieties

We develop a very general version of the hyperbola method which extends the known method by Blomer and Br\"udern 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 $\mathbb{Q}$-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.Comment: 47 pages, Section 4.1 has been added and the main results have been strengthene

Campana points on diagonal hypersurfaces

We construct an integral model for counting Campana points of bounded height on diagonal hypersurfaces of degree greater than one, and give an asymptotic formula for their number, generalising work by Browning and Yamagishi. The paper also includes background material on the theory of Campana points on hyperplanes and previous results in the field.Comment: 19 page