Comptes Rendus
Research article - Algebraic geometry
Equality in the Miyaoka–Yau inequality and uniformization of non-positively curved klt pairs
Comptes Rendus. Mathématique, Volume 362 (2024) no. S1, pp. 55-81.

Let (X,Δ) be a compact Kähler klt pair, where K X +Δ is ample or numerically trivial, and Δ has standard coefficients. We show that if equality holds in the orbifold Miyaoka–Yau inequality for (X,Δ), then its orbifold universal cover is either the unit ball (ample case) or the affine space (numerically trivial case).

Soit (X,Δ) une paire klt compacte kählérienne pour laquelle K X +Δ est ample ou numériquement trivial, et Δ à coefficients standard. Nous démontrons que, si l’inégalité de Miyaoka–Yau orbifold pour (X,Δ) est une égalité, alors le revêtement universel orbifold de la paire est soit la boule (cas ample), soit l’espace affine (cas numériquement trivial).

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DOI: 10.5802/crmath.599
Classification: 32J27, 14J60
Keywords: Miyaoka–Yau inequality, orbifold uniformization, klt pairs
Mot clés : inégalité de Miyaoka–Yau, uniformisation orbifold, paires klt

Benoît Claudon 1; Patrick Graf 2; Henri Guenancia 3

1 Univ Rennes, CNRS, IRMAR – UMR 6625, 35000 Rennes, France et Institut Universitaire de France
2 Lehrstuhl für Mathematik I, Universität Bayreuth, 95440 Bayreuth, Germany
3 Institut de Mathématiques de Toulouse, Université Paul Sabatier, 31062 Toulouse Cedex 9, France
License: CC-BY 4.0
Copyrights: The authors retain unrestricted copyrights and publishing rights
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Benoît Claudon; Patrick Graf; Henri Guenancia. Equality in the Miyaoka–Yau inequality and uniformization of non-positively curved klt pairs. Comptes Rendus. Mathématique, Volume 362 (2024) no. S1, pp. 55-81. doi : 10.5802/crmath.599. https://comptes-rendus.academie-sciences.fr/mathematique/articles/10.5802/crmath.599/

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