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| Format: | Preprint |
| Published: |
2026
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/2601.12113 |
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Table of 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.