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arXiv · 2105.05136

About $\mathcal{C}^\infty$ foliations by holomorphic curves on complex surfaces

Olivier Thom
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Abstract

We study those real $\mathcal{C}^\infty$ 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.

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Olivier Thom. 2021-05-11. About $\mathcal{C}^\infty$ foliations by holomorphic curves on complex surfaces. https://arxiv.org/abs/2105.05136

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