On the Singularities of Degenerate Abelian Varieties

In 2002, Alexeev provided a modular interpretation for the toroidal compactification of $A_g$ for the 2nd Voronoi fan. In this paper we show that pairs $(X,\Theta)$ in the boundary of this moduli space are semi-log canonical, the analog of log canonical in the non-normal setting. This extends the result of Koll${\'a}$r stating that principally polarized abelian pairs $(X,\Theta)$ are log canonical.