We show that the minimum weight of a weighted blowup of Ad with ε–log canonical singularities is bounded by a constant depending only on ε 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.
ASJC Scopus subject areas
- Geometry and Topology