Higher Du Bois and higher rational singularities of hypersurfaces
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arXiv
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| Format: | Preprint |
| Published: |
2023
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| _version_ | 1866912152515772416 |
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| author | Maxim, Laurenţiu Yang, Ruijie |
| author_facet | Maxim, Laurenţiu Yang, Ruijie |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2301_09084 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | Higher Du Bois and higher rational singularities of hypersurfaces Maxim, Laurenţiu Yang, Ruijie Algebraic Geometry Primary: 14J17, Secondary: 32S35, 32S50, 14C17 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. |
| title | Higher Du Bois and higher rational singularities of hypersurfaces |
| topic | Algebraic Geometry Primary: 14J17, Secondary: 32S35, 32S50, 14C17 |
| url | https://arxiv.org/abs/2301.09084 |