no. 5
Convergence of cscK metrics on smooth minimal models of general type
[Convergence des métriques cscK sur des modèles lisses minimaux de type général]
Liu, Wanxing1
1 Department of Mathematics, Northwestern University, 2033 Sheridan Road, Evanston, IL 60208 (USA)
Annales de l'Institut Fourier, Tome 74 (2024) no. 5, pp. 1851-1880.

On considère des métriques de Kähler à courbure scalaire constante sur une surface lissemodèle minimal de type général dans un voisinage de la classe canonique, qui estla perturbation de la classe canonique par une métrique de Kähler fixe. Nous montrons queles séquences de ces métriques convergent en douceur sur des sous-ensembles compacts loin d’un sous-ensemble. variété à la métrique singuliére de Kähler Einstein dans la classe canonique. Cela confirme partiellement une conjecture de Jian–Shi–Song sur le comportement de convergence detels séquences.

We consider constant scalar curvature Kähler metrics on a smooth minimal model of general type in a neighborhood of the canonical class, which is the perturbation of the canonical class by a fixed Kähler metric. We show that sequences of such metrics converge smoothly on compact subsets away from a subvariety to the singular Kähler–Einstein metric in the canonical class. This confirms partially a conjecture of Jian–Shi–Song about the convergence behavior of such sequences.

Reçu le :
Révisé le :
Accepté le :
Publié le :
DOI : 10.5802/aif.3637
Classification : 32W20
Keywords: Kähler geometry, Constant Scalar Curvature Kähler metric.
Mot clés : Géométrie de Kähler, Courbure scalaire constante Métrique de Kähler.

Liu, Wanxing 1

1 Department of Mathematics, Northwestern University, 2033 Sheridan Road, Evanston, IL 60208 (USA)
Licence : CC-BY-ND 4.0
Droits d'auteur : Les auteurs conservent leurs droits 
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Liu, Wanxing. Convergence of cscK metrics on smooth minimal models of general type. Annales de l'Institut Fourier, Tome 74 (2024) no. 5, pp. 1851-1880. doi : 10.5802/aif.3637. https://aif.centre-mersenne.org/articles/10.5802/aif.3637/

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