Injectivity theorems with multiplier ideal sheaves and their applications
Complex Variables
2015-11-16 v1 Algebraic Geometry
Differential Geometry
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).
Keywords
Cite
@article{arxiv.1511.04226,
title = {Injectivity theorems with multiplier ideal sheaves and their applications},
author = {Shin-ichi Matsumura},
journal= {arXiv preprint arXiv:1511.04226},
year = {2015}
}
Comments
14pages. arXiv admin note: substantial text overlap with arXiv:1406.6132, arXiv:1308.2033