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| Autores principales: | , |
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| Formato: | Preprint |
| Publicado: |
2025
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| Materias: | |
| Acceso en línea: | https://arxiv.org/abs/2506.12288 |
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| _version_ | 1866908461028081664 |
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| author | Hu, Yan Xia, Wei |
| author_facet | Hu, Yan Xia, Wei |
| contents | Given a complex analytic family of complex manifolds, we consider canonical Aeppli deformations of $(p,q)$-forms and study its relations to the varying of dimension of the deformed Aeppli cohomology $\dim H^{\bullet,\bullet}_{Aϕ(t)}(X)$. In particular, we prove the jumping formula for the deformed Aeppli cohomology $H^{\bullet,\bullet}_{Aϕ(t)}(X)$. As a direct consequence, $\dim H^{p,q}_{Aϕ(t)}(X)$ remains constant iff the Bott-Chern deformations of $(n-p,n-q)$-forms and the Aeppli deformations of $(n-p-1,n-q-1)$-forms are canonically unobstructed. Furthermore, the Bott-Chern/Aeppli deformations are shown to be unobstructed if some weak forms of $\partial\bar{\partial}$-lemma is satisfied. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2506_12288 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Deformed Aeppli cohomology: canonical deformations and jumping formulas Hu, Yan Xia, Wei Differential Geometry 32G05, 32A05, 55N99 Given a complex analytic family of complex manifolds, we consider canonical Aeppli deformations of $(p,q)$-forms and study its relations to the varying of dimension of the deformed Aeppli cohomology $\dim H^{\bullet,\bullet}_{Aϕ(t)}(X)$. In particular, we prove the jumping formula for the deformed Aeppli cohomology $H^{\bullet,\bullet}_{Aϕ(t)}(X)$. As a direct consequence, $\dim H^{p,q}_{Aϕ(t)}(X)$ remains constant iff the Bott-Chern deformations of $(n-p,n-q)$-forms and the Aeppli deformations of $(n-p-1,n-q-1)$-forms are canonically unobstructed. Furthermore, the Bott-Chern/Aeppli deformations are shown to be unobstructed if some weak forms of $\partial\bar{\partial}$-lemma is satisfied. |
| title | Deformed Aeppli cohomology: canonical deformations and jumping formulas |
| topic | Differential Geometry 32G05, 32A05, 55N99 |
| url | https://arxiv.org/abs/2506.12288 |