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- W3099693667 abstract "We show that any toroidal DM stack $X$ with finite diagonalizable inertia possesses a maximal toroidal coarsening $X_{tcs}$ such that the morphism $Xto X_{tcs}$ is logarithmically smooth. Further, we use torification results of [AT17] to construct a destackification functor, a variant of the main result of Bergh [Ber17], on the category of such toroidal stacks $X$. Namely, we associate to $X$ a sequence of blowings up of toroidal stacks $widetilde{mathcal{F}}_X:Ylongrightarrow X$ such that $Y_{tc}$ coincides with the usual coarse moduli space $Y_{cs}$. In particular, this provides a toroidal resolution of the algebraic space $X_{cs}$. Both $X_{tcs}$ and $widetilde{mathcal{F}}_X$ are functorial with respect to strict inertia preserving morphisms $X'to X$. Finally, we use coarsening morphisms to introduce a class of non-representable birational modifications of toroidal stacks called Kummer blowings up. These modifications, as well as our version of destackification, are used in our work on functorial toroidal resolution of singularities." @default.
- W3099693667 created "2020-11-23" @default.
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- W3099693667 date "2020-09-18" @default.
- W3099693667 modified "2023-10-17" @default.
- W3099693667 title "Toroidal orbifolds, destackification, and Kummer blowings up" @default.
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- W3099693667 doi "https://doi.org/10.2140/ant.2020.14.2001" @default.
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