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Orbifold stability and
Miyaoka–Yau inequality for minimal pairs
Henri Guenancia and Behrouz Taji |
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Geometry & Topology 26 (2022) 1435–1482
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Abstract |
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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. |
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Keywords
Miayoka-Yau inequality, minimal models, orbifold pairs,
singular Kähler-Einstein metrics
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Mathematical Subject Classification 2010
Primary: 14E20, 14E30, 32Q20
Secondary: 14C15, 14C17, 32Q26, 53C07
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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
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Authors |
| Henri Guenancia | |
| Institut de Mathématiques de
Toulouse Université de Toulouse Toulouse France |
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| https://hguenancia.perso.math.cnrs.fr/ | |
| Behrouz Taji | |
| School of Mathematics and
Statistics The University of Sydney Sydney NSW Australia |
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| http://www.maths.usyd.edu.au/u/behrouzt/ | |
