Mathematical Research Letters
Volume 9, Issue 5, September 2002 pp. 639-650.
Families of supersingular curves in characteristic 2Authors: Jasper Scholten and Hui June Zhu
Author institution: K.U. Leuven, and University of California, Berkeley
Summary: This paper determines normal forms of all hyperelliptic supersingular curves of genus $g$ over an algebraically closed field $F$ of characteristic $2$ for $1\leq g\leq 8$. 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 $c\in\overline\mathbb{F}_2$. Consequently, the paper determines the dimensions of the open locus of hyperelliptic supersingular curves of genus $g\leq 9$ over $\overline\mathbb{F}_2$.
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