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 $\kappa (K_X+S+B)\ge 0$. 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

References in corpus (1)

• Deformations of canonical pairs and Fano varieties

Cited by in corpus (2)

• On Fujita's log spectrum conjecture
• A remark on the abundance conjecture