Translator Disclaimer
2020 On upper bounds of Manin type
Sho Tanimoto
Algebra Number Theory 14(3): 731-761 (2020). DOI: 10.2140/ant.2020.14.731

Abstract

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 28 deformation types of smooth Fano 3-folds of Picard rank 2 following the Mori–Mukai classification. We also find new upper bounds for polarized K3 surfaces S of Picard rank 1 using Bayer and Macrì’s result on the nef cone of the Hilbert scheme of two points on S.

Citation

Download Citation

Sho Tanimoto. "On upper bounds of Manin type." Algebra Number Theory 14 (3) 731 - 761, 2020. https://doi.org/10.2140/ant.2020.14.731

Information

Received: 10 January 2019; Revised: 18 July 2019; Accepted: 13 November 2019; Published: 2020
First available in Project Euclid: 2 July 2020

MathSciNet: MR4113779
Digital Object Identifier: 10.2140/ant.2020.14.731

Subjects:
Primary: 14G05
Secondary: 11G50, 14J28, 14J45

Rights: Copyright © 2020 Mathematical Sciences Publishers

JOURNAL ARTICLE
31 PAGES

This article is only available to subscribers.
It is not available for individual sale.
+ SAVE TO MY LIBRARY

SHARE
Vol.14 • No. 3 • 2020
MSP
Back to Top