3 papers
math.AG2026
A lower bound for the Milnor number of vector fields
Maurício Corrêa, Gilcione Nonato Costa, Alejandra Salamanca Russi
We study holomorphic vector fields whose singular locus contains a smooth positive-dimensional local complete-intersection component. We obtain an exact global formula for its Miln…
math.AG2024
A higher-dimensional Van den Essen type formula for projective foliations and applications
Maurício Corrêa, Gilcione Nonato Costa
Let be a one-dimensional holomorphic foliation on such that , where is a smooth complete intersection variety. We determine and compute the…
math.AG2017
On foliations by curves with singularities of positive dimension
Arturo Fernández-Pérez, Gilcione Nonato Costa
We present enumerative results for holomorphic foliations by curves on , , with singularities of positive dimension. Some of the results presented improve pr…