Geodesic
Characteristic curves of holomorphic foliations
Journal of Singularities, Tome 26 (2023), pp. 76-91

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Let F be a germ of holomorphic foliation with an isolated singularity at 0 in C^2 A characteristic curve of F is a continuous one-dimensional curve tending to 0 in C^2, tangent to F and having some "tame" oscillating behavior, which is a kind of generalization of a separatrix. We define a notion of resolution of the set of characteristic curves of F and show that this process gives another way of obtaining the resolution of singularities of the foliation. 
@article{10_5427_jsing_2023_26e,
     author = {Rudy Rosas},
     title = {Characteristic curves of holomorphic foliations},
     journal = {Journal of Singularities},
     pages = {76--91},
     publisher = {mathdoc},
     volume = {26},
     year = {2023},
     doi = {10.5427/jsing.2023.26e},
     url = {http://geodesic.mathdoc.fr/articles/10.5427/jsing.2023.26e/}
}
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Rudy Rosas. Characteristic curves of holomorphic foliations. Journal of Singularities, Tome 26 (2023), pp. 76-91. doi: 10.5427/jsing.2023.26e

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