The supersingular loci and mass formulas on Siegel modular varieties

Abstract

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 ${\mathcal{A}}_{g,1,N}$ for arbitrary $g$.