Algebra & Number Theory
- Algebra Number Theory
- Volume 14, Number 3 (2020), 731-761.
On upper bounds of Manin type
We introduce a certain birational invariant of a polarized algebraic variety and use that to obtain upper bounds for the counting functions of rational points on algebraic varieties. Using our theorem, we obtain new upper bounds of Manin type for deformation types of smooth Fano -folds of Picard rank following the Mori–Mukai classification. We also find new upper bounds for polarized K3 surfaces of Picard rank using Bayer and Macrì’s result on the nef cone of the Hilbert scheme of two points on .
Algebra Number Theory, Volume 14, Number 3 (2020), 731-761.
Received: 10 January 2019
Revised: 18 July 2019
Accepted: 13 November 2019
First available in Project Euclid: 2 July 2020
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Mathematical Reviews number (MathSciNet)
Tanimoto, Sho. On upper bounds of Manin type. Algebra Number Theory 14 (2020), no. 3, 731--761. doi:10.2140/ant.2020.14.731. https://projecteuclid.org/euclid.ant/1593655270