From Lie groupoids to resolutions of singularities. Applications to symplectic and Poisson resolutions

2006/10/09 by Camille Laurent-Gengoux, Laurent-Gengoux, Camille
Mathematics · #22A22 #53D20 #53D99 #Advanced Algebra and Geometry #Advanced Topics in Algebra #Differential Geometry (math.DG) #FOS: Mathematics #Homotopy and Cohomology in Algebraic Topology #Symplectic Geometry (math.SG)

paper · pdf · doi:10.48550/arxiv.math/0610288

openalex publication_date 2006/10/09 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We use the techniques of integration of Poisson manifolds into symplectic Lie groupoids to build symplectic resolutions (= desingularizations) of the closure of a symplectic leaf. More generally, we show how Lie groupoids can be used to lift singularities, in particular when one imposes a compatibility condition with an additional structure given by a multi-vector field.

Related

• Multisymplectic geometry and Lie groupoids
• Dimension preserving resolutions of singularities of Poisson structures
• From symplectic groupoids to double structures
• Equivariant resolutions of singularities as differential substacks
• Some title containing the words "homotopy" and "symplectic", e.g. this one