Some criteria for positive forms and applications
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arXiv
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| Hauptverfasser: | , |
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| Format: | Preprint |
| Veröffentlicht: |
2025
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| _version_ | 1866910934201532416 |
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| author | Fagioli, Filippo Mainenti, Asia |
| author_facet | Fagioli, Filippo Mainenti, Asia |
| contents | The aim of this paper is to gain a better understanding of weak and strong positivity for exterior forms on complex vector spaces. We prove a dimensionality reduction argument for positive forms, which allows us to restrict to the case of $(2,2)$-forms in $\mathbb{C}^4$. In this setting, we find criteria for weak positivity based on the associated Hermitian matrix. As an application we prove, by duality, the strong positivity of some families of $(2,2)$-forms, already of interest in works by other authors. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2502_17317 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Some criteria for positive forms and applications Fagioli, Filippo Mainenti, Asia Differential Geometry Complex Variables 15A63 (Primary) 15B57, 32U40 (Secondary) The aim of this paper is to gain a better understanding of weak and strong positivity for exterior forms on complex vector spaces. We prove a dimensionality reduction argument for positive forms, which allows us to restrict to the case of $(2,2)$-forms in $\mathbb{C}^4$. In this setting, we find criteria for weak positivity based on the associated Hermitian matrix. As an application we prove, by duality, the strong positivity of some families of $(2,2)$-forms, already of interest in works by other authors. |
| title | Some criteria for positive forms and applications |
| topic | Differential Geometry Complex Variables 15A63 (Primary) 15B57, 32U40 (Secondary) |
| url | https://arxiv.org/abs/2502.17317 |