The singularities of $A_g^P$
  We complete the proof given earlier by one of us that the singularities of the perfect cone compactification $A_g^P$ of the coarse moduli space $A_g$ of principally polarized abelian $g$-folds are terminal if $g\ge 6$, and canonical if $g=5$. 
J. Armstrong and N. Shepherd-Barron
math.AG