Extension of sections via adjoint ideals

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.

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

References in corpus (3)

• Existence of minimal models for varieties of log general type
• Relative critical exponents, non-vanishing and metrics with minimal singularities
• A Bergman kernel proof of the Kawamata subadjunction theorem

Cited by in corpus (4)

• Bergman kernels and subadjunction
• Canonical singular hermitian metrics on relative logcanonical bundles
• The Minimal Model Program Revisited
• Lecture notes on the Ein-Popa extension result