arXiv subjects
Publications and source records attributed to Eric Schellhammer.
We consider the moduli space $A_{pol}(n)$ of (non-principally) polarised abelian varieties of genus $g\geq3$ with coprime polarisation and full level-$n$ structure. Based upon the analysis of the Tits building in math/0405321, we give an explicit lower bound on $n$ that is sufficient for the compactified moduli space to be of general type if one further explicit condition is satisfied.
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.