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

Volume 19, 1 issue

Volume 18, 12 issues

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
Ethics and policies
Peer-review process
 
Submission guidelines
Submission form
Editorial board
Editors' interests
 
Subscriptions
 
ISSN 1944-7833 (online)
ISSN 1937-0652 (print)
 
Author index
To appear
 
Other MSP journals
Separation of periods of quartic surfaces

Pierre Lairez and Emre Can Sertöz
Vol. 17 (2023), No. 10, 1753–1778
DOI: 10.2140/ant.2023.17.1753
Abstract

We give a computable lower bound for the distance between two distinct periods of a given quartic surface defined over the algebraic numbers. The main ingredient is the determination of height bounds on components of the Noether–Lefschetz loci. This makes it possible to study the Diophantine properties of periods of quartic surfaces and to certify a part of the numerical computation of their Picard groups.

Keywords
K3 surfaces, periods, Diophantine approximation, Hodge loci, effective mathematics
Mathematical Subject Classification
Primary: 14Q10, 14J28, 32G20
Secondary: 11Y16, 14Q20, 11J99
Milestones
Received: 18 June 2021
Revised: 19 May 2022
Accepted: 21 September 2022
Published: 19 September 2023
Authors
Pierre Lairez
INRIA Saclay
Palaiseau
France
Emre Can Sertöz
Faculty of Mathematics and Physics
Leibniz Universität Hannover
Hannover
Germany
© 2023 MSP (Mathematical Sciences Publishers). Distributed under the Creative Commons Attribution License 4.0 (CC BY).

Open Access made possible by participating institutions via Subscribe to Open.