Higher Du Bois and higher rational singularities of hypersurfaces

Laurenţiu Maxim; Ruijie Yang

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arXiv · 2301.09084

Higher Du Bois and higher rational singularities of hypersurfaces

Laurenţiu Maxim·Ruijie Yang

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Abstract

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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Laurenţiu Maxim, Ruijie Yang. 2023-01-22. Higher Du Bois and higher rational singularities of hypersurfaces. https://arxiv.org/abs/2301.09084

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