Log pluricanonical representations and abundance conjecture
  We prove the finiteness of log pluricanonical representations for projective log canonical pairs with semi-ample log canonical divisor. As a corollary, we obtain that the log canonical divisor of a projective semi log canonical pair is semi-ample if and only if so is the log canonical divisor of its normalization. We also treat many other applications. 
Osamu Fujino, Yoshinori Gongyo
math.AG