Hyperelliptic supersingular curves over fields of characteristic 2

In this paper we prove that there are no hyperelliptic supersin-gular curves over F 2 of genus 2 h − 1 for any integer h ≥ 2. For any natural number g let HSg be the intersection of the supersingular locus with the open hyperelliptic Torelli locus in the moduli space of principally polarized abelian varieties over F 2 of dimensions g. We show that dim HSg = 2 for g = 4, 5 and 6. We exhibit the 2-parameter families of hyperelliptic supersingular curves over F 2 of genus 4, 5 and 6.