4 papers
Birationally integrable vector fields on complex projective surfaces
David MarÃn, Marcel Nicolau
A rational vector field on a complex projective smooth surface is said to be birationally integrable if it generates, by integration, a one-parameter subgroup of the group $\op…
Fake saddles and their transition maps
David MarÃn
We study degenerate singular points of planar vector fields inside a (degenerated) flow-box. These kind of singularities are called fake saddles and their linear parts are always z…
Indices of holomorphic foliations and the bifurcation conjecture
Maycol Falla Luza, Arturo Fernández-Pérez, David MarÃn +1
In this paper, we revisit local invariants (Gómez-Mont-Seade-Verjovsky, variation, Camacho-Sad and Baum-Bott indices) associated with singular holomorphic foliations on $(\mathbb{…
The cyclicity of hyperbolic hemicycles
David MarÃn, Jordi Villadelprat
We consider families of planar polynomial vector fields of degree and study the cyclicity of a type of unbounded polycycle~ called hemicycle. Compactified to the Poincaré…