Title: On Nash blowup of Lie algebroids and singular foliations
Abstract: We prove that any Lie algebroid A admits a Nash-type blow-up Nash(A) that sits in a nice short exact sequence of Lie algebroids 0 → K → Nash(A) → D → 0 with K a Lie algebra bundle and D a Lie algebroid whose anchor map is injective on an open dense subset. The base variety of Nash(A) is a blowup determined by the singular foliation of A. This construction is inspired by the work of O. Mohsen, applied in non-commutative geometry, and by a classical method developed by the mathematician J. Nash, primarily used in algebraic geometry for desingularization. We provide concrete examples.
https://arxiv.org/abs/2404.08840