Topological Abel-Jacobi Map and Mixed Hodge Structures
Fuente:
arXiv
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| Formato: | Preprint |
| Publicado: |
2021
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| _version_ | 1866912213419163648 |
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| author | Zhang, Yilong |
| author_facet | Zhang, Yilong |
| contents | For a smooth projective variety X of dimension 2n-1 over complex field, Zhao defined the topological Abel-Jacobi map, which sends vanishing cycles on a smooth hyperplane section Y to the middle dimensional primitive intermediate Jacobian of X. It agrees with Griffiths' Abel-Jacobi map on vanishing cycles that are algebraic and varies holomorphically on the locus of Hodge classes as hyperplane section deforms. On the other hand, Schnell proposed an alternative construction using the real-splitting property of the mixed Hodge structure on H^{2n-1}(X\Y). We show that the two definitions coincide, which answers a question of Schnell. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2109_05717 |
| institution | arXiv |
| publishDate | 2021 |
| record_format | arxiv |
| spellingShingle | Topological Abel-Jacobi Map and Mixed Hodge Structures Zhang, Yilong Algebraic Geometry Algebraic Topology 14C30, 14H40 Primary, 14F40, 55M05 Secondary For a smooth projective variety X of dimension 2n-1 over complex field, Zhao defined the topological Abel-Jacobi map, which sends vanishing cycles on a smooth hyperplane section Y to the middle dimensional primitive intermediate Jacobian of X. It agrees with Griffiths' Abel-Jacobi map on vanishing cycles that are algebraic and varies holomorphically on the locus of Hodge classes as hyperplane section deforms. On the other hand, Schnell proposed an alternative construction using the real-splitting property of the mixed Hodge structure on H^{2n-1}(X\Y). We show that the two definitions coincide, which answers a question of Schnell. |
| title | Topological Abel-Jacobi Map and Mixed Hodge Structures |
| topic | Algebraic Geometry Algebraic Topology 14C30, 14H40 Primary, 14F40, 55M05 Secondary |
| url | https://arxiv.org/abs/2109.05717 |