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On the Tits building of paramodular groups. (English) Zbl 1177.51011
Summary: We investigate the Tits buildings of the paramodular groups with or without canonical level structure, respectively. These give important combinatorical information about the boundary of the toroidal compactification of the moduli spaces of non-principally polarised abelian varieties.
We give a full classification of the isotropic lines for all of these groups. Furthermore, for square-free, coprime polarisations without level structure we show that there is only one top-dimensional isotropic subspace. In a sequel to this paper we will use this information to establish a general type result for the moduli-space of non-principally polarised abelian varieties with full level structure.

MSC:
51E24 Buildings and the geometry of diagrams
14K10 Algebraic moduli of abelian varieties, classification
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