Theta nullvalues of supersingular Abelian varieties

Abstract

Let η be a polarization with connected kernel on a superspecial abelian variety Eg. We give a sufficient criterion which allows the computation of the theta nullvalues of any quotient of Eg by a maximal isotropic subgroup scheme of ker⁡(η) effectively.This criterion is satisfied in many situations studied by Li and Oort (1998). We used our method to implement an algorithm that computes supersingular curves of genus 3.