Zobrazeno 1 - 9
of 9
pro vyhledávání: '"Louis, Ruben"'
These lecture notes attempt to invite the reader towards the theory of singular foliations, both smooth and holomorphic. In addition to a systematic review of the foundations, and an attempt to put in order examples and several elementary constructio
Externí odkaz:
http://arxiv.org/abs/2407.14932
Autor:
Louis, Ruben
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 $\mathca
Externí odkaz:
http://arxiv.org/abs/2404.08840
Autor:
Louis, Ruben
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 introduce
Externí odkaz:
http://arxiv.org/abs/2301.08706
Autor:
Louis, Ruben
The results of this manuscript is the collection of my articles that I published during my PhD thesis. We show that there is an equivalence of categories between Lie-Rinehart algebras over a commutative algebra $\mathcal O$ and homotopy equivalence c
Externí odkaz:
http://arxiv.org/abs/2301.08335
Autor:
Louis, Ruben
This paper shows that a weak symmetry action of a Lie algebra $\mathfrak{g}$ on a singular foliation $\mathcal F$ induces a unique up to homotopy Lie$\infty$-morphism from $\mathfrak{g}$ to the DGLA of vector fields on a universal Lie $\infty$-algebr
Externí odkaz:
http://arxiv.org/abs/2203.01585
Autor:
Laurent-Gengoux, Camille, Louis, Ruben
We show that there is an equivalence of categories between Lie-Rinehart algebras over a commutative algebra $\mathcal O $ and homotopy equivalence classes of negatively graded Lie $\infty $-algebroids over their resolutions (=acyclic Lie $\infty$-alg
Externí odkaz:
http://arxiv.org/abs/2106.13458
Autor:
Laurent-Gengoux, Camille, Louis, Ruben
Publikováno v:
In Journal of Algebra 15 March 2022 594:1-53
Autor:
Louis, Ruben
We use the universal Lie $\infty$-algebroid of a singular foliation to construct several notions of resolution of singularities. For instance, we recover Nash modification or the monoidal transformation of an affine variety and a resolution method du
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=doi_dedup___::bd3980c1438bcbfd464bb5748ae3cacb
http://arxiv.org/abs/2301.08706
http://arxiv.org/abs/2301.08706