Supersingular curves of genus four in characteristic two

Pub Date : 2024-04-12 DOI:10.1090/proc/16792

Dušan Dragutinović

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引用次数: 1

Abstract

We describe the intersection of the Torelli locus j ( M 4 c t ) = J 4 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 S 4 ∩ J 4 \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 F 2 \mathbb {F}_2 , and another involves a more careful study of some relevant Ekedahl-Oort loci.

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特性二的四属超弦曲线

我们描述了与特征 2 中的超星点相关的牛顿和埃克达尔-奥尔特地层与托雷利点 j ( M 4 c t ) = J 4 j(\mathcal {M}_4^{ct}) = \mathcal {J}_4 的交集。我们证明了在特征 2 中超共轭雅各布数 S 4 ∩ J 4 \mathcal {S}_4\cap \mathcal {J}_4 的位置是纯三维的。要得到这个结果，一种方法是分析定义在 F 2 \mathbb {F}_2 上的光滑四属曲线和主要极化无边四褶的数据，另一种方法是对一些相关的埃克达尔-奥尔特（Ekedahl-Oort）位点进行更细致的研究。

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