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

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

2006-10-09

arxiv.org/abs/math/0610288v2

Mathematics

Differential Geometry

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

Scientific paper

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.

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