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Higher Du Bois and higher rational singularities of hypersurfaces

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arxiv 2301.09084 v4 pith:OTLURX5R submitted 2023-01-22 math.AG

Laurenţiu Maxim , Ruijie Yang This is my paper · ORCID
classification math.AG
keywords highersingularitiesboisrationalhodgehypersurfacesapplicationcharacteristic
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In this note, we give several equivalent characterizations of higher Du Bois and higher rational singularities in the context of globally defined hypersurfaces. As a key input, we characterize these singularities using the Hodge filtration on the vanishing cycle mixed Hodge module. As an application, we indicate a homological criterion for detecting higher Du Bois and higher rational hypersurface singularities, formulated in terms of the spectral Hirzebruch-Milnor characteristic classes.

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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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