Versions of injectivity and extension theorems

Abstract

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 hyperKähler manifolds.

21 pages. v2: The exposition of the proof of Corollary 4.3 is improved. arXiv admin note: text overlap with arXiv:1308.2033