Supersingular curves of genus four in characteristic two

Dragutinović, Dušan

doi:10.1090/proc/16792

Supersingular curves of genus four in characteristic two
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by Dušan Dragutinović;

Proc. Amer. Math. Soc. 152 (2024), 2333-2347

DOI: https://doi.org/10.1090/proc/16792

Published electronically: April 12, 2024

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Abstract:

We describe the intersection of the Torelli locus $j(\mathcal {M}_4^{ct}) = \mathcal {J}_4$ with Newton and Ekedahl-Oort strata related to the supersingular locus in characteristic 2. We show that the locus of supersingular Jacobians $\mathcal {S}_4\cap \mathcal {J}_4$ in characteristic 2 is pure of dimension three. One way to obtain that result uses an analysis of the data of smooth genus four curves and principally polarized abelian fourfolds defined over $\mathbb {F}_2$, and another involves a more careful study of some relevant Ekedahl-Oort loci.

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