Orbifold stability and Miyaoka–Yau inequality for minimal pairs

Guenancia, Henri¹ ; Taji, Behrouz²

¹ Institut de Mathématiques de Toulouse, Université de Toulouse, Toulouse, France
² School of Mathematics and Statistics, The University of Sydney, Sydney NSW, Australia

Geometry & topology, Tome 26 (2022) no. 4, pp. 1435-1482.

Résumé

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.

Détail

DOI : 10.2140/gt.2022.26.1435

Classification : 14E20, 14E30, 32Q20, 14C15, 14C17, 32Q26, 53C07
Keywords: Miayoka-Yau inequality, minimal models, orbifold pairs, singular Kähler-Einstein metrics

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