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Holomorphic foliations tangent to Rolle-pfaffian hypersurfaces [PDF]
Arturo Fernández-Pérez +2 more
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Bounds and formulas for residues of singular holomorphic foliations and applications [PDF]
Diogo da Silva Machado
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Note on Holomorphic Foliations with Turbulences on Elliptic Surfaces
, 2003 Yoshiaki Fukuma +2 more
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Differentiable Invariants of Holomorphic Foliations
Bulletin of the Brazilian Mathematical Society, New Series, 2022zbMATH Open Web Interface contents unavailable due to conflicting licenses.
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HOLOMORPHIC FOLIATIONS AND CHARACTERISTIC NUMBERS
Communications in Contemporary Mathematics, 2005We relate the characteristic numbers of the normal sheaf of a k-dimensional holomorphic foliation [Formula: see text] of a compact complex manifold Mn, to the characteristic numbers of the normal sheaf of a one-dimensional holomorphic foliation associated to [Formula: see text].
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On deformations of transversely holomorphic foliations.
Journal für die reine und angewandte Mathematik (Crelles Journal), 1983A transversally holomorphic foliation F on a compact differentiable manifold X is given by an open covering \(\{U_ i\}\) of X, differentiable submersions \(f_ i:U_ i\to {\mathbb{C}}^ n\), and biholomorphic mappings \(g_{ij}\) of \(f_ j(U_ i\cap U_ j)\) onto \(f_ i(U_ i\cap U_ j)\) such that \(f_ i=g_{ij}{\mathbb{O}}f_ j\). In the paper under review the
Girbau, J. +2 more
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Holomorphic Foliations and the Kobayashi Metric
Proceedings of the American Mathematical Society, 1977Here we extend the notion of the Kobayashi metric from complex manifolds to holomorphic foliations of smooth manifolds. This gives a notion of a hyperbolic foliation. We prove that a hyperbolic foliation of a compact manifold is compact and Hausdorff.
Duchamp, T., Kalka, M.
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Singular holomorphic foliations
1984A generalized Nash Blow-up M' with respect to coherent subsheaves of locally free sheaves is defined for complex spaces. It is shown that M' is locally isomorphic to a monoidal transformation and hence is analytic. Examples of M' are given. Applications are given to Serre's extension problem and reductive group actions. A C* action on Grassmannians are
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Characteristic curves of holomorphic foliations
Journal of Singularities, 2023Summary: Let \(\mathcal{F}\) be a germ of holomorphic foliation with an isolated singularity at \(0 \in \mathbb{C}^2\). A characteristic curve of \(\mathcal{F}\) is a continuous one-dimensional curve tending to \(0 \in \mathbb{C}^2\), tangent to \(\mathcal{F}\) and having some ``tame'' oscillating behavior, which is a kind of generalization of a ...
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