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

  • Torsten EkedahlEmail author
  • Gerard van der Geer
Part of the Progress in Mathematics book series (PM, volume 269)


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. We study its geometric properties, such as 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.

Key words

moduli space abelian variety E-O-stratification cycle classes Weyl group 


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Copyright information

© Springer Science+Business Media, LLC 2009

Authors and Affiliations

  1. 1.Matematiska institutionenStockholms universitetStockholmSweden
  2. 2.Korteweg-de Vries InstituutUniversiteit van AmsterdamAmsterdamThe Netherlands

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