On Finiteness of B-representation and Semi-log Canonical Abundance
  We give a new proof of the finiteness of B-representations. As a consequence of the finiteness of B-representations and Koll\'ar's gluing theory on lc centers, we prove that the (relative) abundance conjecture for slc pairs is implied by the abundance conjecture for log canonical pairs. 
Christopher Hacon, Chenyang Xu
math.AG