Versions of injectivity and extension theorems
  We give an analytic version of the injectivity theorem by using multiplier ideal sheaves, and prove some extension theorems for the adjoint bundle of dlt pairs. Moreover, by combining techniques of the minimal model program, we obtain some results for semi-ampleness related to the abundance conjecture in birational geometry and the Strominger-Yau-Zaslow conjecture for hyperK\"ahler manifolds. 
Yoshinori Gongyo, Shin-ichi Matsumura
math.AG math.CV