Hirzebruch-Milnor classes of local complete intersections, minimal exponent, and applications to higher singularities
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arXiv
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| Format: | Preprint |
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2025
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| _version_ | 1866929707149164544 |
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| author | Dirks, Bradley Maxim, Laurenţiu Olano, Sebastián |
| author_facet | Dirks, Bradley Maxim, Laurenţiu Olano, Sebastián |
| contents | In this paper we use the deformation to the normal cone and the corresponding Verdier-Saito specialization to define and study (spectral) Hirzebruch-Milnor type homology characteristic classes for local complete intersections. Our main results describe vanishing properties of these classes in relation to the minimal exponent. As applications, we show how Hirzebruch-Milnor classes of local complete intersections with a projective singular locus can be used to detect higher Du Bois and higher rational singularities. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2502_06537 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Hirzebruch-Milnor classes of local complete intersections, minimal exponent, and applications to higher singularities Dirks, Bradley Maxim, Laurenţiu Olano, Sebastián Algebraic Geometry Primary: 14J17, Secondary: 32S35, 32S50, 14C17 In this paper we use the deformation to the normal cone and the corresponding Verdier-Saito specialization to define and study (spectral) Hirzebruch-Milnor type homology characteristic classes for local complete intersections. Our main results describe vanishing properties of these classes in relation to the minimal exponent. As applications, we show how Hirzebruch-Milnor classes of local complete intersections with a projective singular locus can be used to detect higher Du Bois and higher rational singularities. |
| title | Hirzebruch-Milnor classes of local complete intersections, minimal exponent, and applications to higher singularities |
| topic | Algebraic Geometry Primary: 14J17, Secondary: 32S35, 32S50, 14C17 |
| url | https://arxiv.org/abs/2502.06537 |