5 papers
On the k-th Milnor and k-th Tjurina Numbers of a Foliation
Marcela Ribeiro, Arturo Fernández-Pérez
In this paper, we introduce the notions of the -th Milnor number and the -th Tjurina number for a germ of holomorphic foliation on the complex plane with an isolated singular…
A Morse-Bott normal form for real analytic Levi-flat hypersurfaces
Arturo Fernández-Pérez, Gustavo Marra
We prove the existence of a normal form for a real-analytic Levi-flat hypersurface defined by the vanishing of the real part of a holomorphic function with a Morse-Bott singularity…
Indices of holomorphic foliations and the bifurcation conjecture
Maycol Falla Luza, Arturo Fernández-Pérez, David Marín +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{C…
The Bruce-Roberts Tjurina number of holomorphic 1-forms along complex analytic varieties
Pedro Barbosa, Arturo Fernández-Pérez, Víctor León
We introduce the notion of the Bruce-Roberts Tjurina number for holomorphic 1-forms relative to a pair of complex analytic subvarieties. When the pair consists of i…
The Bruce-Roberts number of holomorphic 1-forms along complex analytic varieties
Pedro Barbosa, Arturo Fernández-Pérez, Víctor León
We introduce the notion of the \textit{Bruce-Roberts number} for holomorphic 1-forms relative to complex analytic varieties. Our main result shows that the Bruce-Roberts number of…