About $\mathcal{C}^\infty$ foliations by holomorphic curves on complex surfaces
Complex Variables
2021-05-12 v1 Dynamical Systems
Abstract
We study those real foliations in complex surfaces whose leaves are holomorphic curves. The main motivation is to try and understand these foliations in neighborhoods of curves: can we expect the space of foliations in a fixed neighborhood to be infinite-dimensional, or are there some contexts under which every such foliation is holomorphic? We give some restrictions and study in more details the geometry of foliations whose leaves belong to a holomorphic family of holomorphic curves. In particular, we classify all real-analytic foliations on neighborhoods of curves which are locally diffeomorphic to foliations by lines, under some non-degeneracy hypothesis.
Keywords
Cite
@article{arxiv.2105.05136,
title = {About $\mathcal{C}^\infty$ foliations by holomorphic curves on complex surfaces},
author = {Olivier Thom},
journal= {arXiv preprint arXiv:2105.05136},
year = {2021}
}