Abstract: We show that the minimum weight of a weighted blowup of Ad with [epsilon]- log canonical singularities is bounded by a constant depending only on [epsilon] and d . This was conjectured by Birkar. Using the recent classification of 4_ dimensional empty simplices by Iglesias-Valiño and Santos, we work out an explicit bound for blowups of A4 with terminal singular-ities: the smallest weight is always at most 32, and at most 6 in all but finitely many cases.

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