arXiv subjects

Yukiko Sakai

Publications and source records attributed to Yukiko Sakai.

2 recordsLinked to original sources

arXiv2014

Genus 3 curves whose Jacobians have endomorphisms by $Q(ζ_7 + \overlineζ_7)$

In this work we consider constructions of genus three curves $X$ such that $\mathrm{End}(\mathrm{Jac}(X)) \otimes Q$ contains the totally real cubic number field $Q(ζ_ 7 + \overlineζ_7)$. We construct explicit two-dimensional families defined over $Q(s; t)$ whose generic member is a nonhyperelliptic genus 3 curve with this property. The case when X is hyperelliptic was studied by the authors Hoffman and Wang in a previous work. We calculate the zeta function of one of these curves. Conjecturally this zeta function is described by a modular form.

math.AG↗

arXiv2014

Genus 3 curves whose Jacobians have endomorphisms by $Q (ζ_7 +\barζ_7 )$, II

In this work we consider constructions of genus three curves $X$ such that $\mathrm{End}(\mathrm{Jac} (X))\otimes Q$ contains the totally real cubic number field $Q(ζ_7 +\barζ_7 )$. We construct explicit three-dimensional families whose generic member is a nonhyperelliptic genus 3 curve with this property. The case when $X$ 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.

math.AG↗