English

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 XX such that End(Jac(X))Q\mathrm{End}(\mathrm{Jac} (X))\otimes Q contains the totally real cubic number field Q(ζ7+ζˉ7)Q(\zeta _7 +\bar{\zeta}_7 ). We construct explicit three-dimensional families whose generic member is a nonhyperelliptic genus 3 curve with this property. The case when XX 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}
}