Extension of sections via adjoint ideals
Algebraic Geometry
2009-12-20 v3 Complex Variables
Abstract
The paper contains theorems on extending sections of line bundles from divisors to the ambient space, inspired by various results of Siu, Kawamata, and especially Hacon-McKernan and Takayama. Applications are given to basepoint-freeness, to the invariance of analogues of plurigenera and of part of the boundary of the pseudo-effective cone in families, and to a simplified approach towards part of the results used for proving the existence of flips by Hacon-McKernan.
Cite
@article{arxiv.0811.4290,
title = {Extension of sections via adjoint ideals},
author = {Lawrence Ein and Mihnea Popa},
journal= {arXiv preprint arXiv:0811.4290},
year = {2009}
}
Comments
28 pages; v.3: quite a few corrections with respect to the previous version, especially in the statements of Thm. F, Lemma 5.6 and Thm.5.8, and the proof of Cor.C; we also introduced outlines of the proofs of Thm. A and Thm.7.1 in order to make them more user friendly