Hodge decomposition for Kato manifolds
Fuente:
arXiv
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| Format: | Preprint |
| Published: |
2026
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| _version_ | 1866908773290868736 |
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| author | Perri, Giacomo |
| author_facet | Perri, Giacomo |
| contents | We prove that any Kato manifold satisfies the Hodge decomposition, in the sense that $b_k=\sum_{p+q=k}h^{p, q}$, by relating its cohomology to the corresponding cohomology of its modification data. We give, therefore, more evidence supporting a conjecture of Ornea--Verbitsky stating that compact locally conformally Kähler manifolds satisfy the Hodge decomposition. We further study Bott--Chern and Aeppli cohomology of Kato manifolds, showing that in certain degrees they coincide with Dolbeault cohomology. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2601_12113 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Hodge decomposition for Kato manifolds Perri, Giacomo Differential Geometry 53C55, 32J18 We prove that any Kato manifold satisfies the Hodge decomposition, in the sense that $b_k=\sum_{p+q=k}h^{p, q}$, by relating its cohomology to the corresponding cohomology of its modification data. We give, therefore, more evidence supporting a conjecture of Ornea--Verbitsky stating that compact locally conformally Kähler manifolds satisfy the Hodge decomposition. We further study Bott--Chern and Aeppli cohomology of Kato manifolds, showing that in certain degrees they coincide with Dolbeault cohomology. |
| title | Hodge decomposition for Kato manifolds |
| topic | Differential Geometry 53C55, 32J18 |
| url | https://arxiv.org/abs/2601.12113 |