Supersingular Curves of Genus Four in Characteristic Two

Research output: Contribution to journalArticleAcademicpeer-review

Abstract

We describe the intersection of the Torelli locus j(Mct4 )=J4 with Newton and Ekedahl-Oort strata related to the supersingular locus in characteristic 2. We show that the locus of supersingular Jacobians S4 ∩ J4 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 F2, and another involves a more careful study of some relevant Ekedahl-Oort loci.
Original languageEnglish
Pages (from-to)2333-2347
Number of pages15
JournalProceedings of the American Mathematical Society
Volume152
Issue number6
Early online date12 Apr 2024
DOIs
Publication statusPublished - 12 Apr 2024

Bibliographical note

Publisher Copyright:
©2024 American Mathematical Society.

Funding

Received by the editors June 14, 2023, and, in revised form, September 29, 2023, October 24, 2023, and November 3, 2023. 2020 Mathematics Subject Classification. Primary 14H10, 14H40, 11G20, 11G10, 11M38. Key words and phrases. Supersingular, curves, genus four, Jacobians, finite fields, Ekedahl-Oort types. The author was supported by the Mathematical Institute of Utrecht University.

FundersFunder number
Mathematical Institute of Utrecht University

    Keywords

    • EkedahlOort types
    • Jacobians
    • Supersingular
    • Curves
    • Finite fields
    • Genus four
    • finite fields
    • curves
    • Ekedahl-Oort types
    • genus four

    Fingerprint

    Dive into the research topics of 'Supersingular Curves of Genus Four in Characteristic Two'. Together they form a unique fingerprint.

    Cite this