Kähler-Einstein metrics on Fano manifolds. II: Limits with cone angle less than 2
By Xiuxiong Chen, Simon Donaldson, Song Sun. 2012
369 citations recorded by the source corpus.
This is the second of a series of three papers which provide proofs of results announced in arXiv:1210.7494. 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.
Subfields: Applied Mathematics, Geometry and Topology
View Paper: https://www.semanticscholar.org/paper/34e8a3a68f69c4ed43ceaeb5e7609296855a58a0
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In Applied Mathematics
In Geometry and Topology
Citations in the corpus
- Gromov–Hausdorff limits of Kähler manifolds with Ricci curvature bounded below (2018, result): “The argument in Section 3 uses the recent estimates of Cheeger-Jiang-Naber [8], but we show in the Appendix that our results can be obtained independently of [8] by following the approach of Chen-DonaldsonSun [12].”
- Uniform stability of twisted constant scalar curvature K\"ahler metrics (2014, methodology): “1 provides another result which would be required in adapting the methods of [9, 7, 8, 51] to the Aubin continuity method.”
- Kähler–Einstein Metrics on Stable Varieties and log Canonical Pairs (2013, positive): “As for the converse it was finally settled very recently in the deep works by Chen-Donaldson-Sun [ CDS15a, CDS15b, CDS15c ] and Tian [ Tia15 ], independently, in the case when X is smooth.”