L² extension of adjoint line bundle sections

2008/02/21 by Dano Kim, Kim, Dano · 2 citations
Mathematics · #Algebraic Geometry (math.AG) #Algebraic Geometry and Number Theory #Complex Variables (math.CV) #FOS: Mathematics #Geometry and complex manifolds #Homotopy and Cohomology in Algebraic Topology

paper · pdf · doi:10.48550/arxiv.0802.3189

openalex publication_date 2008/02/21 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We prove an L² extension theorem of Ohsawa-Takegoshi type for extending holomorphic sections of line bundles from a subvariety which is given as a maximal log-canonical center of a pair and is of general codimension in a projective variety. Our method of proof indicates that such a setting is the most natural one in a sense, for general L² extension of line bundle sections.

Citations

• A General Non-Vanishing Theorem and an Analytic Proof of the Finite Generation of the Canonical Ring
• Bergman kernels and the pseudoeffectivity of relative canonical bundles
• On the extension ofL 2 holomorphic functions

Cited by

• The exactness of a general Skoda complex
• An extension theorem in terms of adjoint ideal sheaves

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