Genus 3 curves whose Jacobians have endomorphisms by $Q (\zeta _7 +\bar{\zeta}_7 )$, II
Algebraic Geometry
2014-11-11 v1
Abstract
In this work we consider constructions of genus three curves such that contains the totally real cubic number field . We construct explicit three-dimensional families whose generic member is a nonhyperelliptic genus 3 curve with this property. The case when is hyperelliptic was studied in a previous work by Hoffman and Wang and some nonhyperelliptic curves were constructed in a previous paper by Hoffman, Z. Liang. Sakai and Wang.
Keywords
Cite
@article{arxiv.1411.2152,
title = {Genus 3 curves whose Jacobians have endomorphisms by $Q (\zeta _7 +\bar{\zeta}_7 )$, II},
author = {J. W. Hoffman and Dun Liang and Zhibin Liang and Ryotaro Okazaki and Yukiko Sakai and Haohao Wang},
journal= {arXiv preprint arXiv:1411.2152},
year = {2014}
}