Blowups with log canonical singularities

Abstract

We show that the minimum weight of a weighted blow-up of ${\mathbf{A}}^d$ 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 ${\mathbf{A}}^4$ with terminal singularities: the smallest weight is always at most $32$, and at most $6$ in all but finitely many cases.

Sections 3.3 and 3.4 are completely new, and give a proof of Conjecture 1.2 (Birkar) in the general case. Title changed to reflect the increased generality. Minor changes and restructuring in other places

References in corpus (1)

• The complete classification of empty lattice $4$-simplices

Cited by in corpus (2)

• On singularities of threefold weighted blowups
• Sarkisov links from toric weighted blowups of ${\mathbb{P}}^3$ and ${\mathbb{P}}^4$ at a point