Vol. 14, No. 3, 2020

Download this article
Download this article For screen
For printing
Recent Issues

Volume 18
Issue 6, 1039–1219
Issue 5, 847–1038
Issue 4, 631–846
Issue 3, 409–629
Issue 2, 209–408
Issue 1, 1–208

Volume 17, 12 issues

Volume 16, 10 issues

Volume 15, 10 issues

Volume 14, 10 issues

Volume 13, 10 issues

Volume 12, 10 issues

Volume 11, 10 issues

Volume 10, 10 issues

Volume 9, 10 issues

Volume 8, 10 issues

Volume 7, 10 issues

Volume 6, 8 issues

Volume 5, 8 issues

Volume 4, 8 issues

Volume 3, 8 issues

Volume 2, 8 issues

Volume 1, 4 issues

The Journal
About the Journal
Editorial Board
Editors’ Interests
Submission Guidelines
Submission Form
Policies for Authors
Ethics Statement
ISSN: 1944-7833 (e-only)
ISSN: 1937-0652 (print)
Author Index
To Appear
Other MSP Journals
This article is available for purchase or by subscription. See below.
On upper bounds of Manin type

Sho Tanimoto

Vol. 14 (2020), No. 3, 731–761

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.

PDF Access Denied

We have not been able to recognize your IP address as that of a subscriber to this journal.
Online access to the content of recent issues is by subscription, or purchase of single articles.

Please contact your institution's librarian suggesting a subscription, for example by using our journal-recom­mendation form. Or, visit our subscription page for instructions on purchasing a subscription.

You may also contact us at contact@msp.org
or by using our contact form.

Or, you may purchase this single article for USD 40.00:

heights, counting rational points, weak Manin conjecture
Mathematical Subject Classification 2010
Primary: 14G05
Secondary: 11G50, 14J28, 14J45
Received: 10 January 2019
Revised: 18 July 2019
Accepted: 13 November 2019
Published: 1 June 2020
Sho Tanimoto
Department of Mathematics, Faculty of Science
Kumamoto University