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

2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/142453We 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.Paper rewritten. Examples added, some proofs simplified, and a converse theorem addedDifferential GeometrySymplectic Geometry53D99,53D20,22A22From Lie groupoids to resolutions of singularities. Applications to symplectic and Poisson resolutionstext