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

Abstract

We prove an extension theorem for effective purely log-terminal pairs (X, S + B) of non-negative Kodaira dimension κ (KX+S+B)≥ 0. The main new ingredient is a refinement of the Ohsawa-Takegoshi L 2 extension theorem involving singular Hermitian metrics. © 2013 Institut Mittag-Leffler.