Theta Nullvalues of Supersingular Abelian varieties

Abstract

Let $\eta$ be a polarization with connected kernel on a superspecial abelian variety $E^g$. We give a sufficient criterion which allows the computation of the theta nullvalues of any quotient of $E^g$ by a maximal isotropic subgroup scheme of $\ker (\eta )$ effectively. This criterion is satisfied in many situations studied by Li and Oort. We used our method to implement an algorithm that constructs supersingular curves of genus 3.

Source code available at https://github.com/Andreas-Pieper/SuperTheta