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Families of supersingular curves in characteristic 2

Jasper Scholten·Hui June Zhu
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Abstract

This paper determines the normal forms of hyperelliptic supersingular curves of genus g over an algebraically closed field F of characteristic 2 for 0 < g< 9. We also show that every hyperelliptic supersingular curve of genus 9 over F has an equation y^2-y=x^19+c^8x^9+c^3x for some c in F_2bar. The paper determines the dimensions of the open locus of hyperelliptic supersingular curves of genus g < 10 over F_2bar.

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Jasper Scholten, Hui June Zhu. 2001-12-09. Families of supersingular curves in characteristic 2. https://arxiv.org/abs/math/0112086

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