Mathematical Research Letters

Volume 9 (2002)

Number 5

Families of supersingular curves in characteristic 2

Pages: 639 – 650

DOI: http://dx.doi.org/10.4310/MRL.2002.v9.n5.a7

Authors

Jasper Scholten (K.U. Leuven)

Hui June Zhu (University of California at Berkeley)

Abstract

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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