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

Institute of Algebraic Geometry

Inria Saclay Centre

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

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.

Original language	English
Pages (from-to)	1753-1778
Number of pages	26
Journal	Algebra & number theory
Volume	17
Issue number	10
DOIs	https://doi.org/10.48550/arXiv.2011.12316 https://doi.org/10.2140/ant.2023.17.1753
Publication status	Published - 19 Sept 2023

Keywords

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

ASJC Scopus subject areas

Algebra and Number Theory

Access to Document

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

Cite this

@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 -

Separation of periods of quartic surfaces

Abstract

Keywords

ASJC Scopus subject areas

Access to Document

Other files and links

Cite this