Universal flattening of frobenius

For a variety X of positive characteristic and a nonnegative integer e, we define its e-th Fblowup to be the universal flattening of the e-iterated Frobenius of X. Thus we have the sequence (a set labeled by nonnegative integers) of blowups of X. Under some condition, the sequence stabilizes and leads to a nice (for instance, minimal or crepant) resolution. For tame quotient singularities, the sequence leads to the G-Hilbert scheme.