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Let Y be a hypersurface in projective space having only ordinary doublepoints as singularities. We prove a variant of a conjecture of L. Wotzlaw on analgebraic description of the graded quotients of the Hodge filtration on thetop cohomology of the complement of Y except for certain degrees of the gradedquotients, as well as its extension to the Milnor cohomology of a definingpolynomial of Y for degrees a little bit lower than the middle. These partiallygeneralize theorems of Griffiths and Steenbrink in the Y smooth case, andenable us to determine the structure of the pole order spectral sequence. Wethen get quite simple formulas for the Steenbrink and pole order spectra inthis case, which cannot be extended even to the simple singularity case easily.

Generalization of theorems of Griffiths and Steenbrink to hypersurfaces with ordinary double points