Duality between Bott-Chern and Aeppli Cohomology on Non-Compact Complex Manifolds
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arXiv
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| Format: | Preprint |
| Published: |
2026
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| _version_ | 1866909983271026688 |
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| author | Wu, Xiaojun |
| author_facet | Wu, Xiaojun |
| contents | In this paper we establish duality theorems relating Bott-Chern and Aeppli cohomology, both with and without compact support, on non-compact complex manifolds under suitable pseudoconvexity assumptions. In particular, on Stein manifolds we obtain a full Bott-Chern-Aeppli duality extending Serre duality for Dolbeault cohomology. We also show that these results fail in general without pseudoconvexity assumptions by constructing explicit counterexamples on non-compact complex surfaces. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2601_03529 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Duality between Bott-Chern and Aeppli Cohomology on Non-Compact Complex Manifolds Wu, Xiaojun Complex Variables Algebraic Geometry Primary 32C37, Secondary 32C35, 32L10 In this paper we establish duality theorems relating Bott-Chern and Aeppli cohomology, both with and without compact support, on non-compact complex manifolds under suitable pseudoconvexity assumptions. In particular, on Stein manifolds we obtain a full Bott-Chern-Aeppli duality extending Serre duality for Dolbeault cohomology. We also show that these results fail in general without pseudoconvexity assumptions by constructing explicit counterexamples on non-compact complex surfaces. |
| title | Duality between Bott-Chern and Aeppli Cohomology on Non-Compact Complex Manifolds |
| topic | Complex Variables Algebraic Geometry Primary 32C37, Secondary 32C35, 32L10 |
| url | https://arxiv.org/abs/2601.03529 |