We show that the minimum weight of a weighted blowup of with –log canonical singularities is bounded by a constant depending only on and . This was conjectured by Birkar.
Using the recent classification of –dimensional empty simplices by Iglesias-Valiño and Santos, we work out an explicit bound for blowups of with terminal singularities: the smallest weight is always at most , and at most in all but finitely many cases.
"Blowups with log canonical singularities." Geom. Topol. 25 (4) 2145 - 2166, 2021. https://doi.org/10.2140/gt.2021.25.2145