Hyperbola method on toric varieties
Number Theory
2023-12-12 v3 Algebraic Geometry
Abstract
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 complete smooth split toric varieties. We use it to count Campana points of bounded log-anticanonical height on complete smooth split toric -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.
Keywords
Cite
@article{arxiv.2001.09815,
title = {Hyperbola method on toric varieties},
author = {Marta Pieropan and Damaris Schindler},
journal= {arXiv preprint arXiv:2001.09815},
year = {2023}
}
Comments
48 pages, the main results have been significantly strengthened by removing the former technical assumption 4.14