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2022 Orbifold stability and Miyaoka–Yau inequality for minimal pairs
Henri Guenancia, Behrouz Taji
Geom. Topol. 26(4): 1435-1482 (2022). DOI: 10.2140/gt.2022.26.1435

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.

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Henri Guenancia. Behrouz Taji. "Orbifold stability and Miyaoka–Yau inequality for minimal pairs." Geom. Topol. 26 (4) 1435 - 1482, 2022. https://doi.org/10.2140/gt.2022.26.1435

Information

Received: 31 May 2017; Revised: 17 December 2020; Accepted: 17 April 2021; Published: 2022
First available in Project Euclid: 11 November 2022

Digital Object Identifier: 10.2140/gt.2022.26.1435

Subjects:
Primary: 14E20 , 14E30 , 32Q20
Secondary: 14C15 , 14C17 , 32Q26 , 53C07

Keywords: Miayoka-Yau inequality , minimal models , orbifold pairs , singular Kähler-Einstein metrics

Rights: Copyright © 2022 Mathematical Sciences Publishers

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Vol.26 • No. 4 • 2022
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