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

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.

Paper rewritten. Examples added, some proofs simplified, and a converse theorem added

Cited by in corpus (2)

• Equivariant resolutions of singularities as differential substacks
• Dimension preserving resolutions of singularities of Poisson structures