Kähler-Einstein metrics: Old and New

  title={K{\"a}hler-Einstein metrics: Old and New},
  author={Daniele Angella and Cristiano Spotti},
  journal={Complex Manifolds},
  pages={200 - 244}
Abstract We present classical and recent results on Kähler-Einstein metrics on compact complex manifolds, focusing on existence, obstructions and relations to algebraic geometric notions of stability (K-stability). These are the notes for the SMI course "Kähler-Einstein metrics" given by C.S. in Cortona (Italy), May 2017. The material is not intended to be original. 

Constant $$\mu $$-Scalar Curvature Kähler Metric—Formulation and Foundational Results

  • E. Inoue
  • Mathematics
    The Journal of Geometric Analysis
  • 2022
We introduce mu-scalar curvature for a K"ahler metric with a moment map mu and start up a study on constant mu-scalar curvature K"ahler metric as a generalization of both cscK metric and

Equivariant stable sheaves and toric GIT

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This is the third and final paper in a series which establish results announced in arXiv:1210.7494. In this paper we consider the Gromov-Hausdorff limits of metrics with cone singularities in the

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We survey recent results on the existence of Kahler-Einstein metrics on certain smoothable Fano varieties, focusing on the importance of such metrics in the construction of compact algebraic moduli

Degeneration of Riemannian metrics under Ricci curvature bounds

These notes are based on the Fermi Lectures delivered at the Scuola Normale Superiore, Pisa, in June 2001. The principal aim of the lectures was to present the structure theory developed by Toby

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We prove that a metric of constant scalar curvature on a polarised Kahler manifold is the limit of metrics induced from a specific sequence of projective embeddings; satisfying a condition introduced


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abstract:We show that any $n$-dimensional Ding semistable Fano manifold $X$ satisfies that the anti-canonical volume is less than or equal to the value $(n+1)^n$. Moreover, the equality holds if and