Extension theorems, Non-vanishing and the existence of good minimal models

Abstract

We prove an extension theorem for effective plt pairs $(X,S+B)$ of non-negative Kodaira dimension $κ(K_X+S+B)\geq 0$. The main new ingredient is a refinement of the Ohsawa-Takegoshi $L^2$ extension theorem involving singular hermitian metrics.

49 pages; The proof of Theorem 1.2 contained an error. This theorem has been removed