  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.
