Generic singularities of holomorphic foliations by curves on ℙⁿ

2024/09/09 by Gehlawat, Sahil, Nguyên, Viêt-Anh
#37A30 (Primary) 57R30 (Secondary) #37F75 #Complex Variables (math.CV) #Differential Geometry (math.DG) #FOS: Mathematics

paper · doi:10.48550/arxiv.2409.06052

Abstract

Let F_d(ℙⁿ) be the space of all singular holomorphic foliations by curves on ℙⁿ (n ≥ 2) with degree d ≥ 1. We show that there is subset S_d(ℙⁿ) of F_d(ℙⁿ) with full Lebesgue measure with the following properties: 1. for every F ∈ S_d(ℙⁿ), all singular points of F are linearizable hyperbolic. 2. If, moreover, d ≥ 2, then every F does not possess any invariant algebraic curve.

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