6 citations · 30 across the 32 of their papers we have counts for
5 papers · 1 filter
Stable singularities of holomorphic vector fields
Victor Leon, Bruno Scardua
We consider germs of holomorphic vector fields with an isolated singularity at the origin . We introduce a notion of stability, similar to "Lyapunov stability". F…
Meagerness of the set of compact leaves for transversely holomorphic foliations
Bruno Scardua
A transversely holomorphic foliation on a compact complex manifold, exhibits a compact stable leaf if and only if the set of compact leaves is not a meager subset of the manifold.
Closed Orbits and Integrability for singularities of complex vector fields in dimension three
Leonardo Câmara, Bruno Scardua
This paper is about the integrability of complex vector fields in dimension three in a neighborhood of a singular point. More precisely, we study the existence of holomorphic first…
Complex polynomial vector fields with many algebraic orbits
Leonardo Câmara, Bruno Scardua
We state some generalizations of a theorem due to G. Darboux, which originally states that a polynomial vector field in the complex plane exhibits a rational first integral and has…
Transversely projective holomorphic foliations with singularities
Bruno Scardua
We study codimension one holomorphic foliations on complex projective spaces and compact manifolds under the assumption that the foliation has a projective transverse structure in…