Constructing all Genus 2 Curves with Supersingular Jacobian

2021/05/28 by Pieper, Andreas · 1 citation
#14Q05 #Algebraic Geometry (math.AG) #FOS: Mathematics

paper · doi:10.48550/arxiv.2105.13752

Abstract

L. Moret-Bailly constructed families \mathfrakC→ ℙ¹ of genus 2 curves with supersingular jacobian. In this paper we first classify the reducible fibers of a Moret-Bailly family using linear algebra over a quaternion algebra. The main result is an algorithm that exploits properties of two reducible fibers to compute a hyperelliptic model for any irreducible fiber of a Moret-Bailly family.

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