Chow cohomology and Lefschetz (1,1)-theorem
Fuente:
arXiv
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| Autores principales: | , |
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| Formato: | Preprint |
| Publicado: |
2025
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| _version_ | 1866908408734547968 |
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| author | Dan, Ananyo Kaur, Inder |
| author_facet | Dan, Ananyo Kaur, Inder |
| contents | Any smooth, projective variety satisfies the Hodge conjecture in codimension one, known as the Lefschetz (1,1) theorem. Totaro formulated a version for singular varieties. He asked whether the natural Bloch-Gillet-Soulé cycle class map from the operational Chow group to the (1,1)-classes in the weight graded piece of the cohomology group is surjective? In this short article, we give a sufficient criterion for this to hold. In particular, we show that several singular varieties with at worst isolated singularities (log canonical, divisorial log terminal, ADE-singularities) satisfy the singular Hodge conjecture in codimension 1. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2506_13220 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Chow cohomology and Lefschetz (1,1)-theorem Dan, Ananyo Kaur, Inder Algebraic Geometry 14C15, 14C30, 32S35, 32G20 Any smooth, projective variety satisfies the Hodge conjecture in codimension one, known as the Lefschetz (1,1) theorem. Totaro formulated a version for singular varieties. He asked whether the natural Bloch-Gillet-Soulé cycle class map from the operational Chow group to the (1,1)-classes in the weight graded piece of the cohomology group is surjective? In this short article, we give a sufficient criterion for this to hold. In particular, we show that several singular varieties with at worst isolated singularities (log canonical, divisorial log terminal, ADE-singularities) satisfy the singular Hodge conjecture in codimension 1. |
| title | Chow cohomology and Lefschetz (1,1)-theorem |
| topic | Algebraic Geometry 14C15, 14C30, 32S35, 32G20 |
| url | https://arxiv.org/abs/2506.13220 |