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arXiv · 2404.08840

On Nash resolution of (singular) Lie algebroids

Ruben Louis
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Abstract

Any Lie algebroid $A$ admits a Nash-type blow-up $\mathrm{Nash}(A)$ that sits in a nice short exact sequence of Lie algebroids $0\rightarrow K\rightarrow \mathrm{Nash}(A)\rightarrow \mathcal{D}\rightarrow 0$ with $K$ a Lie algebra bundle and $\mathcal{D}$ a Lie algebroid whose anchor map is injective on an open dense subset. The base variety is a blowup determined by the singular foliation of $A$. We provide concrete examples. Moreover, we extend the construction following Mohsen's to singular subalgebroids in the sense of Androulidakis-Zambon.

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Ruben Louis. 2024-04-12. On Nash resolution of (singular) Lie algebroids. https://doi.org/10.1007/s00209-025-03817-4

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