Separation of periods of quartic surfaces

Pierre Lairez; Emre Can Sertöz

doi:10.2140/ant.2023.17.1753

Separation of periods of quartic surfaces

Pierre Lairez
, Emre Can Sertöz

INRIA
Leibniz Universität Hannover

Résultats de recherche: Contribution à un journal › Article › Revue par des pairs

Résumé

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.

langue originale	Anglais
Pages (de - à)	1753-1778
Nombre de pages	26
journal	Algebra and Number Theory
Volume	17
Numéro de publication	10
Les DOIs	https://doi.org/10.2140/ant.2023.17.1753
état	Publié - 1 janv. 2023
Modification externe	Oui

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10.2140/ant.2023.17.1753

Contient cette citation

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title = "Separation of periods of quartic surfaces",

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 = "Diophantine approximation, Hodge loci, K3 surfaces, effective mathematics, periods",

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AU - Sertöz, Emre Can

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N2 - 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.

AB - 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.

KW - Diophantine approximation

KW - Hodge loci

KW - K3 surfaces

KW - effective mathematics

KW - periods

U2 - 10.2140/ant.2023.17.1753

DO - 10.2140/ant.2023.17.1753

M3 - Article

AN - SCOPUS:85172683677

SN - 1937-0652

VL - 17

SP - 1753

EP - 1778

JO - Algebra and Number Theory

JF - Algebra and Number Theory

IS - 10

ER -

Separation of periods of quartic surfaces

Résumé

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