The cycle class of the supersingular locus of principally polarized abelian varieties

Author:

Gerard van der Geer, Shushi Harashita

Keyword:

Mathematics, Algebraic Geometry, Algebraic Geometry (math.AG)

journal:

date:

2023-07-25 16:00:00

Abstract

We prove a formula for the cycle class of the supersingular locus in the Chow ring with rational coefficients of the moduli space of principally polarized abelian varieties in characteristic $p$. This formula determines this class as a monomial in the Chern classes of the Hodge bundle up to a factor that is a polynomial in $p$. This factor is known for $g\leq 3$. We determine the factor for $g=4$.

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