2014/10/06 by Jean-Stefan Koskivirta, Koskivirta, Jean-Stefan
Mathematics · #11G18 #14G35 #14K10 #20G40 #Advanced Algebra and Geometry #Algebraic Geometry (math.AG) #Algebraic Geometry and Number Theory #FOS: Mathematics #Geometry and complex manifolds
paper · pdf · doi:10.48550/arxiv.1410.1317
openalex publication_date 2014/10/06 · openalex created_date 2016/06/24 · openalex updated_date 2026/07/28
We construct canonical non-vanishing global sections of powers of the Hodge bundle on each Ekedahl-Oort stratum of a Hodge type Shimura variety. In particular we recover the quasi-affineness of the Ekedahl-Oort strata. In the projective case, this gives a very short proof of non-emptiness of Ekedahl-Oort strata. It follows that the Newton strata are also nonempty, by a result of S.Nie. We also deduce the fact that the μ-ordinary locus is determined by the Ekedahl-Oort strata of its image by any embedding.