Canonical sections of the Hodge bundle over Ekedahl-Oort strata of Shimura varieties of Hodge type

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. From the canonicity of our construction, we deduce the fact that the mu-ordinary locus is determined by the Ekedahl-Oort strata of its image under any embedding of Shimura varieties. (C) 2015 Elsevier Inc. All rights reserved.