Hyperbola method on toric varieties

Marta Pieropan; Damaris Schindler

doi:10.48550/arXiv.2001.09815

Hyperbola method on toric varieties

Marta Pieropan, Damaris Schindler

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Research output: Working paper › Preprint › Academic

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.

Original language	English
Publisher	arXiv
Pages	1-47
DOIs	https://doi.org/10.48550/arXiv.2001.09815
Publication status	Published - 27 Jan 2020

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2001.09815v2Submitted manuscript, 528 KB
2001.09815Submitted manuscript, 528 KB

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AB - 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.

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Hyperbola method on toric varieties

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