Extension of sections via adjoint ideals

Details Extension of sections via adjoint ideals Extension of sections via adjoint ideals

2008-11-26

arxiv.org/abs/0811.4290v3

Mathematics

Algebraic Geometry

28 pages; v.3: quite a few corrections with respect to the previous version, especially in the statements of Thm. F, Lemma 5.6

Scientific paper

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.

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