On foliations by curves with singularities of positive dimension

Abstract

We present enumerative results for holomorphic foliations by curves on ${\mathbb{P}}^n$, $n\ge 3$, with singularities of positive dimension. Some of the results presented improve previous ones due to Corrêa--Fernández-Pérez--Nonato Costa--Vidal Martins and Nonato Costa. We also present an enumerative result bounding the number of isolated singularities in a projective subvariety invariant by a holomorphic foliation by curves on ${\mathbb{P}}^n$ with a singularity of positive dimension.

28 pages