K3 surfaces with real or complex multiplication

Matthias Schütt; Lambertus  van Geemen; Eva Bayer Fluckiger

doi:10.48550/arXiv.2401.04072

K3 surfaces with real or complex multiplication

Matthias Schütt, Lambertus van Geemen, Eva Bayer Fluckiger

Institute of Algebraic Geometry

Research output: Working paper/Preprint › Preprint

Abstract

Let E be a totally real number field of degree d and let m≥3 be an integer. We show that if md≤21 then there exists an m−2-dimensional family of complex projective K3 surfaces with real multiplication by E. An analogous result is proved for CM number fields.

Original language	English
Number of pages	10
DOIs	https://doi.org/10.48550/arXiv.2401.04072
Publication status	E-pub ahead of print - 8 Jan 2024

Access to Document

10.48550/arXiv.2401.04072Licence: Arxiv nonexclusive-distrib 1.0

Cite this

@techreport{b94b0c8270ed49caa0b15b467b96b332,

title = "K3 surfaces with real or complex multiplication",

abstract = "Let E be a totally real number field of degree d and let m≥3 be an integer. We show that if md≤21 then there exists an m−2-dimensional family of complex projective K3 surfaces with real multiplication by E. An analogous result is proved for CM number fields. ",

author = "Matthias Sch{\"u}tt and {van Geemen}, Lambertus and {Bayer Fluckiger}, Eva",

year = "2024",

month = jan,

day = "8",

doi = "10.48550/arXiv.2401.04072",

language = "English",

type = "WorkingPaper",

}

TY - UNPB

T1 - K3 surfaces with real or complex multiplication

AU - Schütt, Matthias

AU - van Geemen, Lambertus

AU - Bayer Fluckiger, Eva

PY - 2024/1/8

Y1 - 2024/1/8

N2 - Let E be a totally real number field of degree d and let m≥3 be an integer. We show that if md≤21 then there exists an m−2-dimensional family of complex projective K3 surfaces with real multiplication by E. An analogous result is proved for CM number fields.

AB - Let E be a totally real number field of degree d and let m≥3 be an integer. We show that if md≤21 then there exists an m−2-dimensional family of complex projective K3 surfaces with real multiplication by E. An analogous result is proved for CM number fields.

U2 - 10.48550/arXiv.2401.04072

DO - 10.48550/arXiv.2401.04072

M3 - Preprint

BT - K3 surfaces with real or complex multiplication

ER -