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

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 of dimension g 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 $$g\le 3$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mrow> <mml:mi>g</mml:mi> <mml:mo>≤</mml:mo> <mml:mn>3</mml:mn> </mml:mrow> </mml:math> . We also determine the factor for $$g=4$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mrow> <mml:mi>g</mml:mi> <mml:mo>=</mml:mo> <mml:mn>4</mml:mn> </mml:mrow> </mml:math> .