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We show that it is possible to utilize the Hirzebruch-Milnor classes ofprojective hypersurfaces in the classical sense to detect higher du Bois orrational singularities only in some special cases. We also give several remarksclarifying some points in my earlier papers.

Examples of Hirzebruch-Milnor classes of projective hypersurfaces detecting higher du Bois or rational singularities