Extension of sections via adjoint ideals

Lawrence Ein; Mihnea Popa

doi:10.1007/s00208-011-0639-2

Extension of sections via adjoint ideals

Lawrence Ein, Mihnea Popa^*

^*Corresponding author for this work

Mathematics

Research output: Contribution to journal › Article › peer-review

5 Scopus citations

Abstract

We prove theorems on extending sections of line bundles from divisors to the ambient space, inspired by various results of Siu, Kawamata, and especially Hacon-M ^cKernan and Takayama. We include applications 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 slightly simplified approach to results of Hacon-M ^cKernan towards the existence of flips.

Original language	English (US)
Pages (from-to)	373-408
Number of pages	36
Journal	Mathematische Annalen
Volume	352
Issue number	2
DOIs	https://doi.org/10.1007/s00208-011-0639-2
State	Published - Feb 2012

Funding

LE was partially supported by the NSF grant DMS-0700774. MP was partially supported by the NSF grant DMS-0601252 and by a Sloan Fellowship.

ASJC Scopus subject areas

General Mathematics

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10.1007/s00208-011-0639-2

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author = "Lawrence Ein and Mihnea Popa",

note = "Funding Information: LE was partially supported by the NSF grant DMS-0700774. MP was partially supported by the NSF grant DMS-0601252 and by a Sloan Fellowship.",

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AB - We prove theorems on extending sections of line bundles from divisors to the ambient space, inspired by various results of Siu, Kawamata, and especially Hacon-M cKernan and Takayama. We include applications 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 slightly simplified approach to results of Hacon-M cKernan towards the existence of flips.

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Extension of sections via adjoint ideals

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