5 papers
Excess logarithmic residues for foliations by curves and applications
Alana Cavalcante, Maurício Corrêa, Fernando Lourenço +1
We introduce excess logarithmic residues for one-dimensional holomorphic foliations tangent to a divisor. They arise from the comparison between the logarithmic normal sheaf and th…
Split distributions on Grassmann manifolds and smooth quadric hypersurfaces
Alana Cavalcante, Fernando Lourenço
This work is dedicated to studying holomorphic distributions on Grassmann manifolds and smooth quadric hypersurfaces. In special, we prove, under certain conditions, when the tange…
Log Baum--Bott Residues for foliations by curves
Maurício Corrêa, Fernando Lourenço, Diogo Machado
We prove a Baum--Bott type residual formula for one-dimensional holomorphic foliations, and logarithmic along free divisors. More precisely, this provides a Baum--Bott theorem for…
On flags of holomorphic foliations associated with singular second-order ordinary differential equations
Fernando Lourenço, Eurípedes da Silva, Fernando Reis
We consider germs of holomorphic vector fields at the origin of , with non-isolated singularities that are tangent to a holomorphic foliation of codimension one. This…
A brief introduction on residue theory of holomorphic foliations
Fernando Lourenço, Fernando Reis
This is a survey paper dealing with holomorphic foliations, with emphasis on residue theory and its applications. We start recalling the definition of holomorphic foliations as a s…