Geodesic
Kähler-Einstein metrics on Fano manifolds. II: Limits with cone angle less than \boldmath2𝜋
Chen, Xiuxiong1 ; Donaldson, Simon2 ; Sun, Song2
1 Department of Mathematics, Stony Brook University, Stony Brook, New York 11794-3651 – and – School of Mathematics, University of Science and Technology of China, Hefei, Anhui, 230026, PR China
2 Department of Mathematics, Imperial College London, London, U.K.
Journal of the American Mathematical Society, Tome 28 (2015) no. 1, pp. 199-234

Voir la notice de l'article provenant de la source American Mathematical Society

This is the second of a series of three papers which prove the fact that a K-stable Fano manifold admits a Kähler-Einstein metric. In this paper we consider the Gromov-Hausdorff limits of metrics with cone singularities in the case when the limiting cone angle is less than 2${\pi }$. We show that these are in a natrual way projective algebraic varieties. In the case when the limiting variety and the limiting divisor are smooth we show that the limiting metric also has standard cone singularities.
DOI : 10.1090/S0894-0347-2014-00800-6

Chen, Xiuxiong 1 ; Donaldson, Simon 2 ; Sun, Song 2

1 Department of Mathematics, Stony Brook University, Stony Brook, New York 11794-3651 – and – School of Mathematics, University of Science and Technology of China, Hefei, Anhui, 230026, PR China
2 Department of Mathematics, Imperial College London, London, U.K. 
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Chen, Xiuxiong; Donaldson, Simon; Sun, Song. Kähler-Einstein metrics on Fano manifolds. II: Limits with cone angle less than \boldmath2𝜋. Journal of the American Mathematical Society, Tome 28 (2015) no. 1, pp. 199-234. doi: 10.1090/S0894-0347-2014-00800-6

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