Supersingular curves of genus four in characteristic two

IF 0.8 3区数学 Q2 MATHEMATICS

Proceedings of the American Mathematical Society 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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来源期刊

Proceedings of the American Mathematical Society 数学-数学

CiteScore

1.70

自引率

10.00%

发文量

207

审稿时长

2-4 weeks

期刊介绍： All articles submitted to this journal are peer-reviewed. The AMS has a single blind peer-review process in which the reviewers know who the authors of the manuscript are, but the authors do not have access to the information on who the peer reviewers are. This journal is devoted to shorter research articles (not to exceed 15 printed pages) in all areas of pure and applied mathematics. To be published in the Proceedings, a paper must be correct, new, and significant. Further, it must be well written and of interest to a substantial number of mathematicians. Piecemeal results, such as an inconclusive step toward an unproved major theorem or a minor variation on a known result, are in general not acceptable for publication. Longer papers may be submitted to the Transactions of the American Mathematical Society. Published pages are the same size as those generated in the style files provided for AMS-LaTeX.