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

6 Citations (Scopus)

226 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

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AU - Labrande, Hugo

AU - Lercier, Reynald

AU - Ritzenthaler, Christophe

AU - Sijsling, Jeroen

AU - Streng, Marco

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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.

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U2 - 10.4064/aa170227-16-3

DO - 10.4064/aa170227-16-3

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JO - Acta Arithmetica

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