Variation of Hodge structures for non-Kähler manifolds
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arXiv
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| Format: | Preprint |
| Publié: |
2022
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| _version_ | 1866909448111390720 |
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| author | Xia, Wei |
| author_facet | Xia, Wei |
| contents | In this note, we discuss unpolarized, complex variation of Hodge structures for non-Kähler manifolds. In particular, given a holomorphic family of compact complex manifolds whose central fiber satisfies: the inclusions $F^{p}A^{p+q+1}(X)\hookrightarrow A^{p+q+1}(X), F^{p}A^{p+q}(X)\hookrightarrow A^{p+q}(X)$ are injective in cohomology, it is shown that the period map is holomorphic and transversal. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2205_09274 |
| institution | arXiv |
| publishDate | 2022 |
| record_format | arxiv |
| spellingShingle | Variation of Hodge structures for non-Kähler manifolds Xia, Wei Differential Geometry 32G05, 32G20, 55T05 In this note, we discuss unpolarized, complex variation of Hodge structures for non-Kähler manifolds. In particular, given a holomorphic family of compact complex manifolds whose central fiber satisfies: the inclusions $F^{p}A^{p+q+1}(X)\hookrightarrow A^{p+q+1}(X), F^{p}A^{p+q}(X)\hookrightarrow A^{p+q}(X)$ are injective in cohomology, it is shown that the period map is holomorphic and transversal. |
| title | Variation of Hodge structures for non-Kähler manifolds |
| topic | Differential Geometry 32G05, 32G20, 55T05 |
| url | https://arxiv.org/abs/2205.09274 |