Injectivity theorems with multiplier ideal sheaves and their applications

Abstract

The purpose of this survey is to present analytic versions of the injectivity theorem and their applications. The proof of our injectivity theorems is based on a combination of the L^2-method for the dbar-equation and the theory of harmonic integrals. As applications, we obtain Nadel type vanishing theorems and extension theorems for pluri-canonical sections of log pairs. Moreover, we give some results on semi-ampleness related to the abundance conjecture in birational geometry (the minimal model program).

14pages. arXiv admin note: substantial text overlap with arXiv:1406.6132, arXiv:1308.2033

Cited by in corpus (2)

• Injectivity theorem for pseudo-effective line bundles and its applications
• The Kawamata--Viehweg--Nadel-type vanishing theorem and the asymptotic multiplier ideal sheaf