Equivariant resolutions of singularities as differential substacks

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Laurent-Gengoux, Camille
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Abstract
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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).
Comment: 29 pages
Keywords
Mathematics - Differential Geometry, 22A22
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