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

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arxiv 2303.04724 v5 pith:XRQFLNRP submitted 2023-03-08 math.AG

Morihiko Saito This is my paper · ORCID
classification math.AG
keywords boisclasseshigherhirzebruch-milnorhypersurfacesprojectiverationalsingularities
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We show that it is possible to utilize the Hirzebruch-Milnor classes of projective hypersurfaces in the classical sense to detect higher du Bois or rational singularities only in some special cases. We also give several remarks clarifying some points in my earlier papers.

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  1. Hirzebruch-Milnor classes of local complete intersections, minimal exponent, and applications to higher singularities

    math.AG 2025-02 conditional novelty 7.0 of 10

    For lci subvarieties of a smooth variety, spectral Hirzebruch-Milnor classes vanish between bounds set by the minimal exponent, yielding homological criteria for higher singularities.

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