The $\bar\partial$-problem on $Z(q)$-domains
Fuente:
arXiv
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| Autori principali: | , , |
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| Natura: | Preprint |
| Pubblicazione: |
2024
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| _version_ | 1866912980528005120 |
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| author | Chakrabarti, Debraj Harrington, Phillip S. Raich, Andrew |
| author_facet | Chakrabarti, Debraj Harrington, Phillip S. Raich, Andrew |
| contents | Given a complex manifold containing a relatively compact $Z(q)$ domain, we give sufficient geometric conditions on the domain so that its $L^2$-cohomology in degree $(p,q)$ (known to be finite dimensional) vanishes. The condition consists of the existence of a smooth weight function in a neighborhood of the closure of the domain, where the complex Hessian of the weight has a prescribed number of eigenvalues of a particular sign, along with good interaction at the boundary of the Levi form with the complex Hessian, encoded in a subbundle of common positive directions for the two Hermitian forms. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2403_04756 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | The $\bar\partial$-problem on $Z(q)$-domains Chakrabarti, Debraj Harrington, Phillip S. Raich, Andrew Complex Variables 32F10, 32F32, 32W05 Given a complex manifold containing a relatively compact $Z(q)$ domain, we give sufficient geometric conditions on the domain so that its $L^2$-cohomology in degree $(p,q)$ (known to be finite dimensional) vanishes. The condition consists of the existence of a smooth weight function in a neighborhood of the closure of the domain, where the complex Hessian of the weight has a prescribed number of eigenvalues of a particular sign, along with good interaction at the boundary of the Levi form with the complex Hessian, encoded in a subbundle of common positive directions for the two Hermitian forms. |
| title | The $\bar\partial$-problem on $Z(q)$-domains |
| topic | Complex Variables 32F10, 32F32, 32W05 |
| url | https://arxiv.org/abs/2403.04756 |