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Canonical reduction of stabilizers for Artin stacks with good moduli spaces. (arXiv:1710.03220v1 [math.AG])
来源于:arXiv
We prove that if $\mathcal{X}$ is a smooth Artin stack with stable good
moduli space $\mathcal{X} \to X$, then there is a canonical sequence of
birational morphisms of smooth Artin stacks $\mathcal{X}_n \to
\mathcal{X}_{n-1} \to \ldots \to \mathcal{X}_0 = \mathcal{X}$ with the
following properties: (1) the maximum dimension of a stabilizer of a point of
$\mathcal{X}_{k+1}$ is strictly smaller than the maximum dimension of a
stabilizer of $\mathcal{X}_k$ and the final stack $\mathcal{X}_n$ has constant
stabilizer dimension; (2) the morphisms $\mathcal{X}_{k+1} \to \mathcal{X}_k$
induce proper and birational morphisms of good moduli spaces $X_{k+1} \to X_k$;
and (3) the algebraic space $X_n$ has tame quotient singularities and is a
partial desingularization of the good moduli space $X$.
Combining our result with D. Bergh's recent destackification theorem for tame
stacks, we obtain a full desingularization of $X$. 查看全文>>