Around a class version of the Hodge index theorem for singular varieties
Fuente:
arXiv
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| Auteurs principaux: | , , |
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| Format: | Preprint |
| Publié: |
2025
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| _version_ | 1866909899128045568 |
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| author | Aligholi, Mohammadali Maxim, Laurentiu Schuermann, Joerg |
| author_facet | Aligholi, Mohammadali Maxim, Laurentiu Schuermann, Joerg |
| contents | We give an overview of recent developments around a characteristic class version of the Hodge index theorem for singular complex algebraic varieties. This was formulated by Brasselet-Schuermann-Yokura as a conjecture expressing the Goresky-MacPherson homology L-classes in terms of suitable Hodge-theoretic L-classes. Along the way, we clarify the relationship between several notions of L-classes appearing in the literature, but we also include many new cases for which the conjecture is true, e.g., all compact toric varieties, all (matroid) Schubert varieties, all Richardson and intersection varieties, all projective simply connected spherical varieties, and all compact complex algebraic surfaces and threefolds. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2511_08780 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Around a class version of the Hodge index theorem for singular varieties Aligholi, Mohammadali Maxim, Laurentiu Schuermann, Joerg Algebraic Geometry 57R20, 14B05, 32S35, 14C40 We give an overview of recent developments around a characteristic class version of the Hodge index theorem for singular complex algebraic varieties. This was formulated by Brasselet-Schuermann-Yokura as a conjecture expressing the Goresky-MacPherson homology L-classes in terms of suitable Hodge-theoretic L-classes. Along the way, we clarify the relationship between several notions of L-classes appearing in the literature, but we also include many new cases for which the conjecture is true, e.g., all compact toric varieties, all (matroid) Schubert varieties, all Richardson and intersection varieties, all projective simply connected spherical varieties, and all compact complex algebraic surfaces and threefolds. |
| title | Around a class version of the Hodge index theorem for singular varieties |
| topic | Algebraic Geometry 57R20, 14B05, 32S35, 14C40 |
| url | https://arxiv.org/abs/2511.08780 |