Holomorphic vector fields with real integral manifolds
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arXiv
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| Format: | Preprint |
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2024
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| _version_ | 1866929454351122432 |
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| author | Kolář, Martin Kossovskiy, Ilya Lamel, Bernhard |
| author_facet | Kolář, Martin Kossovskiy, Ilya Lamel, Bernhard |
| contents | We classify singular holomorphic vector fields in two-dimensional complex space admitting a (Levi-nonflat) real-analytic invariant 3-fold through the singularity. In this way, we complete the classification of infinitesimal symmetries of real-analytic Levi-nonflat hypersurfaces in complex two-space. The classification of holomorphic vector fields obtained in the paper has very interesting overlaps with the recent Lombardi-Stolovitch classification theory for holomorphic vector fields at a singularity. In particular, we show that most of the resonances arising in Lombardi-Stolovitch theory do not occur under the presence of (Levi-nonflat) integral manifolds. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2408_05186 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Holomorphic vector fields with real integral manifolds Kolář, Martin Kossovskiy, Ilya Lamel, Bernhard Complex Variables Dynamical Systems 32V40, 32H02 We classify singular holomorphic vector fields in two-dimensional complex space admitting a (Levi-nonflat) real-analytic invariant 3-fold through the singularity. In this way, we complete the classification of infinitesimal symmetries of real-analytic Levi-nonflat hypersurfaces in complex two-space. The classification of holomorphic vector fields obtained in the paper has very interesting overlaps with the recent Lombardi-Stolovitch classification theory for holomorphic vector fields at a singularity. In particular, we show that most of the resonances arising in Lombardi-Stolovitch theory do not occur under the presence of (Levi-nonflat) integral manifolds. |
| title | Holomorphic vector fields with real integral manifolds |
| topic | Complex Variables Dynamical Systems 32V40, 32H02 |
| url | https://arxiv.org/abs/2408.05186 |