Separation of periods of quartic surfaces

Pierre Lairez; Emre Can Sertöz

doi:10.48550/arXiv.2011.12316

Separation of periods of quartic surfaces

Pierre Lairez
, Emre Can Sertöz

Institut für Algebraische Geometrie

Inria Saclay Centre

Publikation: Beitrag in Fachzeitschrift › Artikel › Forschung › Peer-Review

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.

Originalsprache	Englisch
Seiten (von - bis)	1753-1778
Seitenumfang	26
Fachzeitschrift	Algebra & number theory
Jahrgang	17
Ausgabenummer	10
DOIs	https://doi.org/10.48550/arXiv.2011.12316 https://doi.org/10.2140/ant.2023.17.1753
Publikationsstatus	Veröffentlicht - 19 Sept. 2023

ASJC Scopus Sachgebiete

Algebra und Zahlentheorie

Zugriff auf Dokument

10.48550/arXiv.2011.12316Lizenz: Arxiv nonexclusive-distrib 1.0
10.2140/ant.2023.17.1753Lizenz: CC BY 4.0

Andere Dateien und Links

Verknüpfung zur Publikation in Scopus

Dieses zitieren

@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",

}

TY - JOUR

T1 - Separation of periods of quartic surfaces

AU - Lairez, Pierre

AU - Sertöz, Emre Can

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 - https://www.scopus.com/pages/publications/85172683677

U2 - 10.48550/arXiv.2011.12316

DO - 10.48550/arXiv.2011.12316

M3 - Article

SN - 1937-0652

VL - 17

SP - 1753

EP - 1778

JO - Algebra & number theory

JF - Algebra & number theory

IS - 10

ER -