Plane quartics over Q with complex multiplication

Pinar Kilicer; Hugo Labrande; Reynald Lercier; Christophe Ritzenthaler; Jeroen Sijsling; Marco Streng

doi:10.4064/aa170227-16-3

Plane quartics over Q with complex multiplication

Pinar Kilicer, Hugo Labrande, Reynald Lercier, Christophe Ritzenthaler, Jeroen Sijsling, Marco Streng

Algebra

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

5 Citations (Scopus)

211 Downloads (Pure)

Abstract

We give examples of smooth plane quartics over $Q$ with complex multiplication over $\overline{Q}$ by a maximal order with primitive CM type. We describe the required algorithms as we go, these involve the reduction of period matrices, the fast computation of Dixmier-Ohno invariants, and reconstruction from these invariants. Finally, we discuss some of the reduction properties of the curves that we obtain.

Original language	English
Pages (from-to)	127-156
Number of pages	25
Journal	Acta Arithmetica
Volume	185
Issue number	2
DOIs	https://doi.org/10.4064/aa170227-16-3
Publication status	Published - 13-Jul-2018

Keywords

math.NT
math.AG

Access to Document

10.4064/aa170227-16-3Licence: CC BY-NC-ND

Plane quartics over Q with complex multiplicationFinal publisher's version, 416 KBLicence: CC BY-NC-ND

Cite this

@article{1aa3d97ea7b049159daacfb9a64a0228,

title = "Plane quartics over Q with complex multiplication",

abstract = " We give examples of smooth plane quartics over $Q$ with complex multiplication over $\overline{Q}$ by a maximal order with primitive CM type. We describe the required algorithms as we go, these involve the reduction of period matrices, the fast computation of Dixmier-Ohno invariants, and reconstruction from these invariants. Finally, we discuss some of the reduction properties of the curves that we obtain. ",

keywords = "math.NT, math.AG",

author = "Pinar Kilicer and Hugo Labrande and Reynald Lercier and Christophe Ritzenthaler and Jeroen Sijsling and Marco Streng",

note = "25 pages",

year = "2018",

month = jul,

day = "13",

doi = "10.4064/aa170227-16-3",

language = "English",

volume = "185",

pages = "127--156",

journal = "Acta Arithmetica",

issn = "0065-1036",

publisher = "Polish Academy of Sciences, Institute of Mathematics",

number = "2",

}

TY - JOUR

T1 - Plane quartics over Q with complex multiplication

AU - Kilicer, Pinar

AU - Labrande, Hugo

AU - Lercier, Reynald

AU - Ritzenthaler, Christophe

AU - Sijsling, Jeroen

AU - Streng, Marco

N1 - 25 pages

PY - 2018/7/13

Y1 - 2018/7/13

N2 - We give examples of smooth plane quartics over $Q$ with complex multiplication over $\overline{Q}$ by a maximal order with primitive CM type. We describe the required algorithms as we go, these involve the reduction of period matrices, the fast computation of Dixmier-Ohno invariants, and reconstruction from these invariants. Finally, we discuss some of the reduction properties of the curves that we obtain.

AB - We give examples of smooth plane quartics over $Q$ with complex multiplication over $\overline{Q}$ by a maximal order with primitive CM type. We describe the required algorithms as we go, these involve the reduction of period matrices, the fast computation of Dixmier-Ohno invariants, and reconstruction from these invariants. Finally, we discuss some of the reduction properties of the curves that we obtain.

KW - math.NT

KW - math.AG

U2 - 10.4064/aa170227-16-3

DO - 10.4064/aa170227-16-3

M3 - Article

VL - 185

SP - 127

EP - 156

JO - Acta Arithmetica

JF - Acta Arithmetica

SN - 0065-1036

IS - 2

ER -