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Specialization of $F$-Zips
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abstract
In \cite{MW}, B. Moonen and the author defined a new invariant, called $F$-Zips, of certain varieties in positive characteristics. We showed that the isomorphism classes of these invariants can be interpreted as orbits of a certain variety $Z$ with an action of a reductive group $G$. In loc. cit. we gave a combinatorial description of the set of these orbits. In this manuscript we give an explicit combinatorial recipe to decide which orbits are in the closure of a given orbit. We do this by relating $Z$ to a semi-linear variant of the wonderful compactification of $G$ constructed by de Concini and Procesi. As an application we give an explicit criterion of the closure relation for Ekedahl-Oort strata in the moduli space of principally polarized abelian varieties.
Forward citations
Cited by 2 Pith papers
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Intersections of the Ekedahl-Oort and Newton Strata of $\mathcal{A}_{5}$
In dimension 5 the non-empty intersections between Ekedahl-Oort and Newton strata of A_g are completely determined, together with the induced Ekedahl-Oort stratification on the supersingular locus S_5.
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Ekedahl-Oort strata under natural embeddings of orthogonal and unitary Shimura varieties
Determines the Ekedahl-Oort strata containing images under natural embeddings of orthogonal and unitary Shimura varieties and computes their discrete invariants.
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