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arXiv · 2507.03519

An unusual family of supersingular curves of genus five in characteristic two

Dušan Dragutinović
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Abstract

We construct a family of smooth supersingular curves of genus $5$ in characteristic $2$ with several notable features: its dimension matches the expected dimension of any component of the supersingular locus in genus $5$, its members are non-hyperelliptic curves with non-trivial automorphism groups, and each curve in the family admits a double cover structure over both an elliptic curve and a genus-$2$ curve. We also provide an explicit parametrization of this family.

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Dušan Dragutinović. 2025-07-04. An unusual family of supersingular curves of genus five in characteristic two. https://arxiv.org/abs/2507.03519

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