#### Volume 25, issue 4 (2021)

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Blowups with log canonical singularities

### Gregory Sankaran and Francisco Santos

Geometry & Topology 25 (2021) 2145–2166
##### Abstract

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

##### Keywords
binational geometry, log canonical singularities, blowups, lattice simplices
##### Mathematical Subject Classification 2010
Primary: 14B05
Secondary: 14E99, 14M25, 52B20