A series of Nash resolutions of a singular foliation

2023/01/20 by Ruben Louis, Louis, Ruben · 1 citation
Mathematics · Physics and Astronomy · #17B66 #18G10 #18G35 #32S45 #53-XX #53C12 #53D17 #Algebraic Geometry and Number Theory #Differential Geometry (math.DG) #FOS: Mathematics #Homotopy and Cohomology in Algebraic Topology #Nonlinear Waves and Solitons

paper · pdf · doi:10.48550/arxiv.2301.08706

openalex publication_date 2023/01/20 · openalex created_date 2023/01/24 · openalex updated_date 2026/07/28

Abstract

We construct a series of blowups (\widetilde M_i,π_i)_{i∈ \mathbb N0} of a singular foliation by applying to the universal Lie ∞-algebroid of a singular foliation the so-called Nash modification. For i=0, we recover a blowup introduced Sinan Sertöz, and for i=1, we recover a notion due to Omar Mohsen. One of the important features is that any singular foliation becomes a Debord foliation (= projective singular foliation) after one blowup. Examples are also given.

Cited by

• On longitudinal differential operators and Nash blowups

Related

• On Nash resolution of (singular) Lie algebroids
• Blown-up singular Riemannian foliations
• Nash blowup fails to resolve singularities in dimensions four and higher
• On longitudinal differential operators and Nash blowups
• On a Computational Approach to the Nash Blowup Problem