An application of adjoint ideal sheaves to injectivity and extension theorems

2023/06/01 by Tsz On Mario Chan, Chan, Tsz On Mario, Young-Jun Choi +1 · 1 citation
Mathematics · #Geometry and complex manifolds #Algebraic Geometry and Number Theory #Geometric and Algebraic Topology

paper · pdf · doi:10.48550/arxiv.2306.00670

Abstract

This note reviews the authors' approach to Fujino's conjecture, i.e. the injectivity theorem for lc pairs on compact Kähler manifolds, via the use of adjoint ideal sheaves coupled with the associated residue computations in their previous work. Using only the techniques and results obtained from that study and under a slightly stronger positivity assumption, a "qualitative" extension result is obtained. Such extension result guarantees the existence of a global holomorphic extension F of any holomorphic section f on some σ-lc centres of the given lc pair. The extension F can be shown to take values in the corresponding adjoint ideal sheaf, even though it comes without any L² estimate of F in terms of f. Moreover, the proof invokes and implies no vanishing theorem in general.

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• An extension theorem in terms of adjoint ideal sheaves

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