Versal deformation of transversely holomorphic flows on the boundary of strongly convex domains of $\mathbb C^n$
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arXiv
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| Format: | Preprint |
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2025
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| _version_ | 1866910002687508480 |
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| author | Abouanass, Mounib |
| author_facet | Abouanass, Mounib |
| contents | In this article, we give a versal deformation for any transversely holomorphic foliation $\mathcal{F}_0$ given by the intersection of the orbits of a holomorphic vector field $ξ$ defined on a neighborhood of the closure of a bounded strongly convex open domain $Ω\subset\mathbb C^n$ ($n\geq2$) with smooth boundary, with its boundary $\partial Ω$. That is, any germ of deformation of $\mathcal{F}_0$ is also obtained by intersecting the orbits of a deformation of $ξ$ with the boundary of $Ω$. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2505_06577 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Versal deformation of transversely holomorphic flows on the boundary of strongly convex domains of $\mathbb C^n$ Abouanass, Mounib Complex Variables Algebraic Topology In this article, we give a versal deformation for any transversely holomorphic foliation $\mathcal{F}_0$ given by the intersection of the orbits of a holomorphic vector field $ξ$ defined on a neighborhood of the closure of a bounded strongly convex open domain $Ω\subset\mathbb C^n$ ($n\geq2$) with smooth boundary, with its boundary $\partial Ω$. That is, any germ of deformation of $\mathcal{F}_0$ is also obtained by intersecting the orbits of a deformation of $ξ$ with the boundary of $Ω$. |
| title | Versal deformation of transversely holomorphic flows on the boundary of strongly convex domains of $\mathbb C^n$ |
| topic | Complex Variables Algebraic Topology |
| url | https://arxiv.org/abs/2505.06577 |