Functorial destackification and weak factorization of orbifolds
arXiv:1905.00872
Abstract
Let X be a smooth and tame stack with finite inertia. We prove that there is a functorial sequence of blow-ups with smooth centers after which the stabilizers of X become abelian. Using this result, we can extend the destackification results of the first author to any smooth tame stack. We give applications to resolution of tame quotient singularities, prime-to-l alterations of singularities and weak factorization of Deligne-Mumford stacks. We also extend the abelianization result to infinite stabilizers in characteristic zero, generalizing earlier work of Reichstein-Youssin.
38 pages
References in corpus (9)
- A Luna étale slice theorem for algebraic stacks
- Existence and properties of geometric quotients
- Smoothness, Semistability, and Toroidal Geometry
- Tannaka Duality for Geometric Stacks
- Functorial destackification of tame stacks with abelian stabilisers
- Factorization for stacks and boundary complexes
- Weak factorization and the Grothendieck group of Deligne-Mumford stacks
- Functorial resolution of tame quotient singularities in positive characteristic
- A generalization of Luna's fundamental lemma for stacks with good moduli spaces