The Supersingular Loci and Mass Formulas on Siegel Modular Varieties

We describe the supersingular locus of the Siegel 3-fold with a parahoric level structure. We also study its higher dimensional generalization. Using this correspondence and a deep result of Li and Oort, we evaluate the number of irreducible components of the supersingular locus of the Siegel moduli space $\calA_{g,1,N}$ for arbitrary $g$.

2000 Mathematics Subject Classification: Primary 11G18; Secondary 14K12.

Keywords and Phrases: Siegel modular varieties, supersingular locus, superspecial locus, parahoric level structure, mass formula

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