Canonical reduction of stabilizers for Artin stacks with good moduli spaces

We present a complete generalization of Kirwan’s partial desingularization theorem on quotients smooth varieties. Precisely, we prove that if X is an irreducible Artin stack with stable good moduli space X→πX, then there canonical sequence birational morphisms stacks Xn→Xn−1→⋯→X0=X the following properties: (1) maximum dimension stabilizer point Xk+1 strictly smaller than Xk and final Xn has constant dimension; (2) Xk+1→Xk induce projective spaces Xk+1→Xk. If in addition smooth, each intermediate gerbe over tame stack. In this case algebraic quotient singularities X. When our result can be combined D. Bergh’s recent destackification for to obtain full