Blowups with log canonical singularities

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

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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

Volume 25, issue 4 (2021)

Gregory Sankaran and Francisco Santos

Abstract