Defines Nash blow-up Nash(A) for Lie algebroids yielding short exact sequence 0 to K to Nash(A) to D to 0 with K Lie algebra bundle and D having dense injective anchor, plus extension to singular subalgebroids.
A series of Nash resolutions of a singular foliation
3 Pith papers cite this work. Polarity classification is still indexing.
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Pith papers citing it
abstract
We construct a series of blowups $(\widetilde M_i,\pi_i)_{i\in \mathbb N_0}$ of a singular foliation by applying to the universal Lie $\infty$-algebroid of a singular foliation the so-called Nash modification. For $i=0$, we recover a blowup introduced Sinan Sert\"oz, 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.
fields
math.DG 3verdicts
UNVERDICTED 3representative citing papers
Links Helffer-Nourrigat cone of singular foliations to Nash algebroids and characterizes longitudinally elliptic operators via symplectic leaves of holonomy Lie algebroids.
Constructs a series of Nash blowups of singular foliations that turn any such foliation into a Debord foliation after one step, recovering prior cases for i=0 and i=1.
citing papers explorer
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On Nash resolution of (singular) Lie algebroids
Defines Nash blow-up Nash(A) for Lie algebroids yielding short exact sequence 0 to K to Nash(A) to D to 0 with K Lie algebra bundle and D having dense injective anchor, plus extension to singular subalgebroids.
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On longitudinal differential operators and Nash blowups
Links Helffer-Nourrigat cone of singular foliations to Nash algebroids and characterizes longitudinally elliptic operators via symplectic leaves of holonomy Lie algebroids.
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A series of Nash resolutions of a singular foliation
Constructs a series of Nash blowups of singular foliations that turn any such foliation into a Debord foliation after one step, recovering prior cases for i=0 and i=1.