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We study the Hodge filtration on the local cohomology sheaves of a smoothcomplex algebraic variety along a closed subscheme Z in terms of logresolutions, and derive applications regarding the local cohomologicaldimension, the Du Bois complex, local vanishing, and reflexive differentialsassociated to Z.

Hodge filtration on local cohomology, Du Bois complex, and local cohomological dimension