An extension theorem in terms of adjoint ideal sheaves

2026/07/31 by Tsz On Mario Chan
Mathematics · #math.CV #math.AG #msc:32J25 #msc:32Q15 #msc:14B05

paper · pdf · doi:10.4036/iis.2026.a.04

published as Interdiscip. Inform. Sci. 32 (2026), no. 1, 1-12 · 16 pages; article in the Proceedings of ICFIDCAA 2024

arxiv created 2026/07/31 · arxiv updated 2026/08/03

Abstract

In the context of the study of the Ohsawa--Takegoshi L² extension theorem, a "qualitative" extension theorem in terms of adjoint ideal sheaves (i.e. extension result without L² estimates but with some form of local L² 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.

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