An exceptional locus in the perfect compactification of $A_g$
  The line bundle $12M-D$ on the perfect compactification $A_g^P$ is nef; we show here that in positive characteristic it is semi-ample and that in all characteristics its exceptional locus is the closure of the locus of abelian varieties with an elliptic factor. 
N. Shepherd-Barron
math.AG