The supersingular loci and mass formulas on Siegel modular varieties

Mathematics – Number Theory

Scientific paper

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Revised version, 18 pages

Scientific paper

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 $g$.

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