Singularities in the Ekedahl--Oort stratification
Fuente:
arXiv
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| Autori principali: | , , |
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| Natura: | Preprint |
| Pubblicazione: |
2025
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| _version_ | 1866915350780575744 |
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| author | Koskivirta, Jean-Stefan La Porta, Lorenzo Reppen, Stefan |
| author_facet | Koskivirta, Jean-Stefan La Porta, Lorenzo Reppen, Stefan |
| contents | We give conceptual and combinatorial criteria for the normality and Cohen--Macaulayness of unions of Ekedahl--Oort strata in the special fiber of abelian type Shimura varieties. For unions of two strata, one of the two having codimension one in the closure of the other, we determine exactly when their union is smooth. We provide explicit numerical criteria for the smoothness of any one-dimensional EO-stratum closure of Shimura varieties. For groups of type $\mathsf{B}_n$, we describe the smooth and normal loci of all EO-strata closures. We construct reduced strata Hasse invariants of explicit weights on EO-strata of codimension at most $n-1$, showing that their Zariski closures are local complete intersections. We also provide a closed form formula for their cycle classes. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2506_16086 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Singularities in the Ekedahl--Oort stratification Koskivirta, Jean-Stefan La Porta, Lorenzo Reppen, Stefan Number Theory Algebraic Geometry 14G35, 14D23, 14B05, 20G40 We give conceptual and combinatorial criteria for the normality and Cohen--Macaulayness of unions of Ekedahl--Oort strata in the special fiber of abelian type Shimura varieties. For unions of two strata, one of the two having codimension one in the closure of the other, we determine exactly when their union is smooth. We provide explicit numerical criteria for the smoothness of any one-dimensional EO-stratum closure of Shimura varieties. For groups of type $\mathsf{B}_n$, we describe the smooth and normal loci of all EO-strata closures. We construct reduced strata Hasse invariants of explicit weights on EO-strata of codimension at most $n-1$, showing that their Zariski closures are local complete intersections. We also provide a closed form formula for their cycle classes. |
| title | Singularities in the Ekedahl--Oort stratification |
| topic | Number Theory Algebraic Geometry 14G35, 14D23, 14B05, 20G40 |
| url | https://arxiv.org/abs/2506.16086 |