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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 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 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
References
Publication
Received: 18 March 2020
Revised: 30 June 2020
Accepted: 30 July 2020
Published: 12 July 2021
Proposed: Mark Gross
Seconded: Dan Abramovich, Walter Neumann
Authors
Gregory Sankaran
Department of Mathematical Sciences
University of Bath
Bath
United Kingdom
Francisco Santos
Departamento de Matemáticas, Estadística y Computación
Facultad de Ciencias
Universidad de Cantabria
Santander
Spain