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Cycles on the Moduli Space of Abelian Varieties

Gerard van der Geer
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Abstract

In this paper a number of results on cycles on the moduli space of principally polarized abelian varieties is presented. Results include a determination of the tautological ring, bounds on the order of torsion of the top Chern class $λ_g$ and a determination of the cycle classes of the Ekedahl-Oort stratification in characteristic $p$. It includes as special cases formulas for the classes of loci like the $p$-rank $\leq f$ locus or the $a$-number $\geq a$-locus. The results on the tautological ring are my own work, the results on the torsion of $λ_g$ and on the cycle classes of the Ekedahl-Oort stratification are joint work with Torsten Ekedahl and some of the results on curves are joint work with Carel Faber.

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Gerard van der Geer. 1996-06-17. Cycles on the Moduli Space of Abelian Varieties. https://arxiv.org/abs/alg-geom/9605011

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