Boundedness of log Calabi-Yau pairs of Fano type
  We prove a boundedness result for klt pairs $(X,B)$ such that $K_X+B\equiv 0$ and $B$ is big. As a consequence we obtain a positive answer to the Effective Iitaka Fibration Conjecture for klt pairs with big boundary. 
Christopher D. Hacon and Chenyang Xu
math.AG