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math.AG2025
Homogeneous Convex Foliations of degree 6
Carla Pracias, Maycol Falla Luza
In this paper, we study homogeneous convex foliations on the complex projective plane . A foliation is called convex if all of its leaves, except straight lines, have…
math.AG2024
Distributions and Legendrian foliations in dimension 3
Maycol Falla Luza, Rudy Rosas
We study the field of rational first integrals of distributions. We show that for a distribution on 3 dimensional manifolds there exists a tangent vector field with the same field…
math.AG2020
Neighborhoods of rational curves without functions
Maycol Falla Luza, Frank Loray
We prove the existence of (non compact) complex surfaces with a smooth rational curve embedded such that there does not exist any formal singular foliation along the curve. In part…