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On an injectivity theorem for log-canonical pairs with analytic adjoint ideal sheaves
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As an application of the residue functions corresponding to the lc-measures developed by the authors, the proof of the injectivity theorem on compact K\"ahler manifolds for plt pairs by Matsumura is improved in this article to allow multiplier ideal sheaves of plurisubharmonic functions with neat analytic singularities in the coefficients of the relevant cohomology groups. With the use of a refined version of analytic adjoint ideal sheaves, a plan towards a solution to the generalised version of Fujino's conjecture (i.e. an injectivity theorem on compact K\"ahler manifolds for lc pairs with multiplier ideal sheaves) is laid down and, in addition to the result for plt pairs, a proof for lc pairs in dimension 2, which is also an improvement of Matsumura's result, is given.
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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).
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