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We show that a polarized affine variety admits a Ricci flat K\"ahler cone metric, if and only if it is K-stable.
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by same author, A Brunn-Minkowski type inequality for Fano manifolds and some uniqueness theorems in Kähler geometry , Invent. Math. 200
2015
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Xiuxiong Chen, Simon Donaldson, and Song Sun, Kähler-Einstein metrics on Fano manifolds. I: Approximation of metrics with cone singularities , J. Amer. Math. Soc. 28
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by same author, Kähler-Einstein metrics on Fano manifolds. II: Limits with cone angle less than 2 π 2\pi , J. Amer. Math. Soc. 28
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R. J. Berman, K-polystability of q-fano varieties admitting kähler-einstein metrics , Inventiones mathematicae 203
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