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 vérifie que est irréductible et est big, alors n’admet pas de métrique Kähler-Einstein conique d’angle sur , quelque soit l’angle rationnel positif 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 satisfies that is irreducible and is big, then does not admit Kähler-Einstein edge metrics with angle along for any sufficiently small positive rational number . This gives an affirmative answer to a conjecture of Cheltsov and Rubinstein.
@article{AFST_2016_6_25_5_1013_0,
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},
number = {5},
year = {2016},
doi = {10.5802/afst.1520},
zbl = {1375.14140},
mrnumber = {3582118},
language = {en},
url = {http://archive.numdam.org/articles/10.5802/afst.1520/}
}
TY - JOUR AU - Fujita, Kento TI - On log K-stability for asymptotically log Fano varieties JO - Annales de la Faculté des sciences de Toulouse : Mathématiques PY - 2016 DA - 2016/// SP - 1013 EP - 1024 VL - Ser. 6, 25 IS - 5 PB - Université Paul Sabatier, Toulouse UR - http://archive.numdam.org/articles/10.5802/afst.1520/ UR - https://zbmath.org/?q=an%3A1375.14140 UR - https://www.ams.org/mathscinet-getitem?mr=3582118 UR - https://doi.org/10.5802/afst.1520 DO - 10.5802/afst.1520 LA - en ID - AFST_2016_6_25_5_1013_0 ER -
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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