On the geometry of thin exceptional sets in Manin’s conjecture

Brian Lehmann; Sho Tanimoto

doi:10.1215/00127094-2017-0011

Abstract

Manin’s conjecture predicts the rate of growth of rational points of a bounded height after removing those lying on an exceptional set. We study whether the exceptional set in Manin’s conjecture is a thin set using the minimal model program and boundedness of log Fano varieties.

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Brian Lehmann. Sho Tanimoto. "On the geometry of thin exceptional sets in Manin’s conjecture." Duke Math. J. 166 (15) 2815 - 2869, 15 October 2017. https://doi.org/10.1215/00127094-2017-0011

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Received: 26 July 2016; Revised: 17 January 2017; Published: 15 October 2017

First available in Project Euclid: 1 September 2017

zbMATH: 06812210

MathSciNet: MR3712166

Digital Object Identifier: 10.1215/00127094-2017-0011

Subjects:

Primary: 14G05

Secondary: 14E30

Keywords: Fano varieties , Manin’s conjecture , minimal model program , rational points

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