Holomorphic vector fields with real integral manifolds
- Author(s)
- Martin Kolář, Ilya Kossovskiy, Bernhard Lamel
- Abstract
We classify singular holomorphic vector fields in C 2 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.
- Organisation(s)
- Department of Mathematics, Faculty of Mathematics
- External organisation(s)
- Masaryk University, Department of Mathematics and Statistics, Southern University of Science and Technology, International Center of Mathematics, Technische Universität Wien
- Journal
- Advances in Mathematics
- Volume
- 482
- ISSN
- 0001-8708
- DOI
- https://doi.org/10.1016/j.aim.2025.110639
- Publication date
- 12-2025
- Peer reviewed
- Yes
- Austrian Fields of Science 2012
- 101002 Analysis
- Keywords
- ASJC Scopus subject areas
- General Mathematics
- Portal url
- https://ucrisportal.univie.ac.at/en/publications/d579a824-8c11-4c68-a57c-92271097d89e