Cycle Classes of the E-O Stratification on the Moduli of Abelian Varieties

Details Cycle Classes of the E-O Stratification on the Moduli of Abelian Varieties Cycle Classes of the E-O Stratification on the Moduli of Abelian Varieties

2004-12-14

arxiv.org/abs/math/0412272v2

Mathematics

Algebraic Geometry

60 pages; At some places Sp was misprinted as Spec. This has been corrected

Scientific paper

We introduce a stratification on the space of symplectic flags on the de Rham bundle of the universal principally polarized abelian variety in positive characteristic and study its geometric properties like irreducibility of the strata and we calculate the cycle classes. When the characteristic $p$ is treated as a formal variable these classes can be seen as a deformation of the classes of the Schubert varieties for the corresponding classical flag variety (the classical case is recovered by putting $p$ equal to 0). We relate our stratification with the E-O stratification on the moduli space of principally polarized abelian varieties of a fixed dimension and derive properties of the latter. Our results are strongly linked with the combinatorics of the Weyl group of the symplectic group.

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