Cycles on the Moduli Space of Abelian Varieties

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 ${\lambda }_g$ 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 $\le f$ locus or the $a$-number $\ge a$-locus. The results on the tautological ring are my own work, the results on the torsion of ${\lambda }_g$ 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.

Plain TeX, 22 pages; an erroneous lemma corrected

References in corpus (1)

• Formulas for Lagrangian and orthogonal degeneracy loci; the Q-polynomials approach

Cited by in corpus (1)

• The p-torsion of curves with large p-rank