Publication details
Holomorphic vector fields with real integral manifolds
| Authors | |
|---|---|
| Year of publication | 2025 |
| Type | Article in Periodical |
| Magazine / Source | ADVANCES IN MATHEMATICS |
| MU Faculty or unit | |
| Citation | |
| web | https://www.sciencedirect.com/science/article/pii/S0001870825005377 |
| Doi | https://doi.org/10.1016/j.aim.2025.110639 |
| Keywords | CR manifolds; Infinitesimal automorphisms; Holomorphic vector fields; Invariant manifolds |
| Description | We classify singular holomorphic vector fields in C2 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. (c) 2025 Elsevier Inc. All rights are reserved, including those for text and data mining, AI training, and similar technologies. |
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