On the supersingular locus of the Siegel modular variety of genus 3 or 4

Ryosuke Shimada; Teppei Takamatsu

On the supersingular locus of the Siegel modular variety of genus 3 or 4

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arxiv 2403.19505 v2 pith:2TJH5ERP submitted 2024-03-28 math.AG math.NT

Ryosuke Shimada , Teppei Takamatsu This is my paper · ORCID

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keywords locussupersingularvarietygenusmodularsiegelaffineconcretely

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We study the supersingular locus of the Siegel modular variety of genus 3 or 4. More concretely, we decompose the supersingular locus into a disjoint union of the product of a Deligne-Lusztig variety of Coxeter type and a finite-dimensional affine space after taking perfection.

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Lifting Deligne-Lusztig Reduction and Geometric Coxeter Type Elements
math.AG 2025-07 conditional novelty 7.0 of 10

A new class of Weyl group elements, geometric Coxeter type, is shown to decompose affine Deligne-Lusztig varieties into classical Deligne-Lusztig varieties times affine spaces and tori.

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