Criterion proven for smooth DM stacks to be weighted blow-ups of another stack under bundle and normal bundle conditions, applied to show stable genus one curve moduli is a weighted blow-up of the pseudo-stable stack.
Olsson, On proper coverings of artin stacks , Advances in Mathematics 198 (2005), no
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A criterion for smooth weighted blow-downs
Criterion proven for smooth DM stacks to be weighted blow-ups of another stack under bundle and normal bundle conditions, applied to show stable genus one curve moduli is a weighted blow-up of the pseudo-stable stack.