Duke Mathematical Journal

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

Brian Lehmann and Sho Tanimoto

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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.

Article information

Duke Math. J., Volume 166, Number 15 (2017), 2815-2869.

Received: 26 July 2016
Revised: 17 January 2017
First available in Project Euclid: 1 September 2017

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Mathematical Reviews number (MathSciNet)

Zentralblatt MATH identifier

Primary: 14G05: Rational points
Secondary: 14E30: Minimal model program (Mori theory, extremal rays)

Manin’s conjecture minimal model program rational points Fano varieties


Lehmann, Brian; Tanimoto, Sho. On the geometry of thin exceptional sets in Manin’s conjecture. Duke Math. J. 166 (2017), no. 15, 2815--2869. doi:10.1215/00127094-2017-0011. https://projecteuclid.org/euclid.dmj/1504252913

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