Subvarieties of Siegel modular varieties of general type. (Q1068904)

Let \(A_ g\) denote the moduli space of principally polarized Abelian varieties of genus \(g\). The main result of the paper is that every subvariety of codimension smaller than \(g-13\) in \(A_ g\) is of general type. Furthermore every divisor of \(A_ g\) is of general type for \(g\geq 10\). The results are obtained by considering tensors on \(A_ g\), which are combinations of Poincaré series and theta series.