On foliations by curves with singularities of positive dimension

2017/11/08 by Fernández-Pérez, Arturo, Costa, Gilcione Nonato
#32S65 #Algebraic Geometry (math.AG) #Complex Variables (math.CV) #FOS: Mathematics

paper · doi:10.48550/arxiv.1711.02906

Abstract

We present enumerative results for holomorphic foliations by curves on ℙⁿ, n≥ 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 ℙⁿ with a singularity of positive dimension.

Related

• Invariant curves for holomorphic foliations on singular surfaces
• Foliations on ℙ² with only one singular point
• Generic singularities of holomorphic foliations by curves on ℙⁿ
• Foliations on Projective Complete Intersection K3 Surfaces
• Invariant theory of foliations of the projective plane