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Separation of periods of quartic surfaces

Pierre Lairez and Emre Can Sertöz

Vol. 17 (2023), No. 10, 1753–1778
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

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