Separation of periods of quartic surfaces

Research output: Contribution to journal › Article › Research › peer review

Authors

  • Pierre Lairez
  • Emre Can Sertöz

Research Organisations

External Research Organisations

  • Inria Saclay Centre
View graph of relations

Details

Original languageEnglish
Pages (from-to)1753-1778
Number of pages26
JournalAlgebra & number theory
Volume17
Issue number10
Publication statusPublished - 19 Sept 2023

Abstract

We give a computable lower bound on 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

    math.AG, math.NT, 14Q10, 14J28, 32G20, 11Y16, 14Q20, 11J99, Hodge loci, Diophantine approximation, periods, effective mathematics, K3 surfaces

ASJC Scopus subject areas

Cite this

Separation of periods of quartic surfaces. / Lairez, Pierre; Sertöz, Emre Can.
In: Algebra & number theory, Vol. 17, No. 10, 19.09.2023, p. 1753-1778.

Research output: Contribution to journal › Article › Research › peer review

Lairez P, Sertöz EC. Separation of periods of quartic surfaces. Algebra & number theory. 2023 Sept 19;17(10):1753-1778. doi: 10.48550/arXiv.2011.12316, 10.2140/ant.2023.17.1753
Lairez, Pierre ; Sertöz, Emre Can. / Separation of periods of quartic surfaces. In: Algebra & number theory. 2023 ; Vol. 17, No. 10. pp. 1753-1778.
Download
@article{5aced062fea243cb823353aafb4bde4b,
title = "Separation of periods of quartic surfaces",
abstract = " We give a computable lower bound on 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 = "math.AG, math.NT, 14Q10, 14J28, 32G20, 11Y16, 14Q20, 11J99, Hodge loci, Diophantine approximation, periods, effective mathematics, K3 surfaces",
author = "Pierre Lairez and Sert{\"o}z, {Emre Can}",
note = "Publisher Copyright: {\textcopyright} 2023 MSP (Mathematical Sciences Publishers).",
year = "2023",
month = sep,
day = "19",
doi = "10.48550/arXiv.2011.12316",
language = "English",
volume = "17",
pages = "1753--1778",
journal = "Algebra & number theory",
issn = "1937-0652",
publisher = "Mathematical Sciences Publishers",
number = "10",

}

Download

TY - JOUR

T1 - Separation of periods of quartic surfaces

AU - Lairez, Pierre

AU - Sertöz, Emre Can

N1 - Publisher Copyright: © 2023 MSP (Mathematical Sciences Publishers).

PY - 2023/9/19

Y1 - 2023/9/19

N2 - We give a computable lower bound on 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 on 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 - math.AG

KW - math.NT

KW - 14Q10, 14J28, 32G20, 11Y16, 14Q20, 11J99

KW - Hodge loci

KW - Diophantine approximation

KW - periods

KW - effective mathematics

KW - K3 surfaces

UR - http://www.scopus.com/inward/record.url?scp=85172683677&partnerID=8YFLogxK

U2 - 10.48550/arXiv.2011.12316

DO - 10.48550/arXiv.2011.12316

M3 - Article

VL - 17

SP - 1753

EP - 1778

JO - Algebra & number theory

JF - Algebra & number theory

SN - 1937-0652

IS - 10

ER -