Volume 25, issue 4 (2021)

Download this article
Download this article For screen
For printing
Recent Issues

Volume 28
Issue 5, 1995–2482
Issue 4, 1501–1993
Issue 3, 1005–1499
Issue 2, 497–1003
Issue 1, 1–496

Volume 27, 9 issues

Volume 26, 8 issues

Volume 25, 7 issues

Volume 24, 7 issues

Volume 23, 7 issues

Volume 22, 7 issues

Volume 21, 6 issues

Volume 20, 6 issues

Volume 19, 6 issues

Volume 18, 5 issues

Volume 17, 5 issues

Volume 16, 4 issues

Volume 15, 4 issues

Volume 14, 5 issues

Volume 13, 5 issues

Volume 12, 5 issues

Volume 11, 4 issues

Volume 10, 4 issues

Volume 9, 4 issues

Volume 8, 3 issues

Volume 7, 2 issues

Volume 6, 2 issues

Volume 5, 2 issues

Volume 4, 1 issue

Volume 3, 1 issue

Volume 2, 1 issue

Volume 1, 1 issue

The Journal
About the Journal
Editorial Board
Editorial Procedure
Subscriptions
 
Submission Guidelines
Submission Page
Policies for Authors
Ethics Statement
 
ISSN 1364-0380 (online)
ISSN 1465-3060 (print)
Author Index
To Appear
 
Other MSP Journals
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