Plane quartics over $\mathbb{Q}$ with complex multiplication
Number Theory
2022-04-11 v4 Algebraic Geometry
Abstract
We give examples of smooth plane quartics over with complex multiplication over 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
Cite
@article{arxiv.1701.06489,
title = {Plane quartics over $\mathbb{Q}$ with complex multiplication},
author = {Pınar Kılıçer and Hugo Labrande and Reynald Lercier and Christophe Ritzenthaler and Jeroen Sijsling and Marco Streng},
journal= {arXiv preprint arXiv:1701.06489},
year = {2022}
}
Comments
25 pages