On log K-stability for asymptotically log Fano varieties
Annales de la Faculté des sciences de Toulouse : Mathématiques, Série 6, Tome 25 (2016) no. 5, pp. 1013-1024.

La notion de variété asymptotiquement log Fano a été proposée par Cheltsov et Rubinstein. Dans ce travail on montre que, si une variété asymptotiquement log Fano (X,D) vérifie que D est irréductible et -K X -D est big, alors X n’admet pas de métrique Kähler-Einstein conique d’angle 2πβ sur D, quelque soit l’angle rationnel positif β suffisamment petit. Ce résultat donne une réponse positive à une conjecture de Cheltsov et Rubinstein.

The notion of asymptotically log Fano varieties was given by Cheltsov and Rubinstein. We show that, if an asymptotically log Fano variety (X,D) satisfies that D is irreducible and -K X -D is big, then X does not admit Kähler-Einstein edge metrics with angle 2πβ along D for any sufficiently small positive rational number β. This gives an affirmative answer to a conjecture of Cheltsov and Rubinstein.

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     author = {Fujita, Kento},
     title = {On log {K-stability} for asymptotically log {Fano} varieties},
     journal = {Annales de la Facult\'e des sciences de Toulouse : Math\'ematiques},
     pages = {1013--1024},
     publisher = {Universit\'e Paul Sabatier, Toulouse},
     volume = {Ser. 6, 25},
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     year = {2016},
     doi = {10.5802/afst.1520},
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Fujita, Kento. On log K-stability for asymptotically log Fano varieties. Annales de la Faculté des sciences de Toulouse : Mathématiques, Série 6, Tome 25 (2016) no. 5, pp. 1013-1024. doi : 10.5802/afst.1520. http://archive.numdam.org/articles/10.5802/afst.1520/

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