AI 中文总结
本文在紧Kähler流形上，借鉴Chan-Choi-Matsumura的单射定理研究方法，通过调和理论与残数计算，证明了以伴随理想层表述的定性扩张定理，可保证线丛值全纯顶形式的存在性。
AI 中文摘要
在Ohsawa-Takegoshi L²扩张定理的研究背景下，本文在紧Kähler流形上通过调和理论与残数计算，证明了一个以伴随理想层表述的“定性”扩张定理，即不含L²估计但确保某种局部L²条件的扩张结果。该论证改编自Chan-Choi-Matsumura对单射定理的研究方法。该结果尤其保证，在适当正性假设下，存在定义在任意相同余维数的对数典范中心之并上的线丛值全纯顶形式，到环境空间顶形式的扩张。
英文摘要
In the context of the study of the Ohsawa--Takegoshi $L^2$ extension theorem, a "qualitative" extension theorem in terms of adjoint ideal sheaves (i.e. extension result without $L^2$ estimates but with some form of local $L^2$ condition ensured) is proved on compact Kähler manifolds via harmonic theory and residue computations. The arguments are adapted from those in the study of the injectivity theorem by Chan--Choi--Matsumura. The result guarantees, in particular, the existence of extensions of line-bundle-valued holomorphic top forms over the union of any log-canonical centres of the same codimension to top forms over the ambient space under suitable positivity assumptions.
Comments16 pages; article in the Proceedings of ICFIDCAA 2024
Journal refInterdiscip. Inform. Sci. 32 (2026), no. 1, 1-12
