Partial desingularizations of good moduli spaces of Artin toric stacks

Dan Edidin; Yogesh More

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arXiv · 1012.1301

Partial desingularizations of good moduli spaces of Artin toric stacks

Dan Edidin·Yogesh More

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Abstract

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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Dan Edidin, Yogesh More. 2010-12-06. Partial desingularizations of good moduli spaces of Artin toric stacks. https://arxiv.org/abs/1012.1301

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