On the Super-Schottky Ideal and Powers of the Classical Schottky Ideal for $g\ge 5$

The super Schottky ideal defines the image of the superperiod map, which takes a family of genus $g$ supercurves to its Jacobian. We prove that if $g\ge 5$, then $d=g$ is the minimal number such that $I_{Sch,g}^d\subset I_{s-Sch,g}$, where $I_{Sch,g}$ is the Schottky ideal and $I_{s-Sch,g}$ is the super Schottky ideal.