Equivariant resolutions of singularities as differential substacks

Abstract

We show that there is an one-to-one correspondence between resolutions (equivariant w.r.t. a Lie groupoid action) of a singular subset of a manifold, and substacks (of a certain type) of the differential stack associated to the Lie groupoid in question. In particular, we show how to build an equivariant resolution out of Lie subgroupoids (of a certain type).