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On Berman-Gibbs stability and K-stability of $\mathbb{Q}$-Fano varieties

Algebraic Geometry 2019-02-20 v1 Differential Geometry

Abstract

The notion of Berman-Gibbs stability was originally introduced by Robert Berman for Q\mathbb{Q}-Fano varieties XX. We show that the pair (X,KX)(X, -K_X) is K-stable (resp. K-semistable) provided that XX is Berman-Gibbs stable (resp. semistable).

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Cite

@article{arxiv.1501.00248,
  title  = {On Berman-Gibbs stability and K-stability of $\mathbb{Q}$-Fano varieties},
  author = {Kento Fujita},
  journal= {arXiv preprint arXiv:1501.00248},
  year   = {2019}
}

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13 pages