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arXiv · 2208.12492

Theta Nullvalues of Supersingular Abelian varieties

Andreas Pieper
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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.

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Andreas Pieper. 2022-08-26. Theta Nullvalues of Supersingular Abelian varieties. https://arxiv.org/abs/2208.12492

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