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

Volume 26
Issue 4, 1435–1905
Issue 3, 937–1434
Issue 2, 477–936
Issue 1, 1–476

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 Interests
Editorial Procedure
Subscriptions
 
Submission Guidelines
Submission Page
Policies for Authors
Ethics Statement
 
ISSN (electronic): 1364-0380
ISSN (print): 1465-3060
Author Index
To Appear
 
Other MSP Journals
Orbifold stability and Miyaoka–Yau inequality for minimal pairs

Henri Guenancia and Behrouz Taji

Geometry & Topology 26 (2022) 1435–1482
Abstract

After establishing suitable notions of stability and Chern classes for singular pairs, we use Kähler–Einstein metrics with conical and cuspidal singularities to prove the slope semistability of orbifold tangent sheaves of minimal log canonical pairs of log general type. We then proceed to prove the Miyaoka–Yau inequality for all minimal pairs with standard coefficients. Our result in particular provides an alternative proof of the abundance theorem for threefolds, which is independent of positivity results for cotangent sheaves established by Miyaoka.

Keywords
Miayoka-Yau inequality, minimal models, orbifold pairs, singular Kähler-Einstein metrics
Mathematical Subject Classification 2010
Primary: 14E20, 14E30, 32Q20
Secondary: 14C15, 14C17, 32Q26, 53C07
References
Publication
Received: 31 May 2017
Revised: 17 December 2020
Accepted: 17 April 2021
Published: 28 October 2022
Proposed: Lothar Göttsche
Seconded: Mark Gross, Dan Abramovich
Authors
Henri Guenancia
Institut de Mathématiques de Toulouse
Université de Toulouse
Toulouse
France
https://hguenancia.perso.math.cnrs.fr/
Behrouz Taji
School of Mathematics and Statistics
The University of Sydney
Sydney NSW
Australia
http://www.maths.usyd.edu.au/u/behrouzt/