On an $$L^2$$ extension theorem from log-canonical centres with log-canonical measures

As an application of the residue functions corresponding to the lc-measures developed by the authors, the proof of the injectivity theorem on compact Kähler 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 Kähler 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 2 , which is also an improvement of Matsumura’s result, is given.

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On an $$L^2$$ extension theorem from log-canonical centres with log-canonical measures

Cited by 2 publications

References 7 publications

A New Definition of Analytic Adjoint Ideal Sheaves via the Residue Functions of Log-Canonical Measures I

A New Definition of Analytic Adjoint Ideal Sheaves via the Residue Functions of Log-Canonical Measures I

On an injectivity theorem for log-canonical pairs with analytic adjoint ideal sheaves

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