Partial desingularizations of good moduli spaces of Artin toric stacks

Details Partial desingularizations of good moduli spaces of Artin toric stacks Partial desingularizations of good moduli spaces of Artin toric stacks

2010-12-06

arxiv.org/abs/1012.1301v3

Mathematics

Algebraic Geometry

25 pages, error corrected in statement of Cor 4.13. To appear in Mich Math Journal

Scientific paper

We define Reichstein transforms to be certain birational transformations of Artin stacks with good moduli spaces. Our main technical result is that the Reichstein transform of an Artin toric stack is again an Artin toric stack. This leads to our main theorem which states that for Artin toric stacks there is a canonical sequence of Reichstein transforms which produces a Deligne-Mumford toric stack. When the good moduli space of an Artin toric stack is projective our procedure can be interpreted in terms of Kirwan's partial desingularization of geometric invariant theory quotients.

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