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Given an n-dimensional variety Z with rational singularities, we conjecture that if f : Y → Z is a resolution of singularities whose reduced exceptional divisor E has simple normal crossings, thenWe prove this when Z has isolated singularities and when it is a toric variety. We deduce that for a divisor D with isolated rational singularities on a smooth complex n-dimensional variety X, the generation level of Saito's Hodge filtration on the localization OX ( * D) is at most n − 3.

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