On compact Kähler manifolds, holomorphic top forms on σ-lc centres of the same codimension extend to the ambient space, without L² estimates, under the curvature positivity condition (eq5.1).
Błocki,Suita conjecture and the Ohsawa-Takegoshi extension theorem, Invent
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An extension theorem in terms of adjoint ideal sheaves
On compact Kähler manifolds, holomorphic top forms on σ-lc centres of the same codimension extend to the ambient space, without L² estimates, under the curvature positivity condition (eq5.1).