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Kähler-Einstein metrics: Old and New
Complex Manifolds, 2017 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).
Angella Daniele, Spotti Cristiano
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Singular Kähler-Einstein metrics and RCD spaces
Forum of Mathematics, PiWe study Kähler-Einstein metrics on singular projective varieties. We show that under an approximation property with constant scalar curvature metrics, the metric completion of the smooth part is a noncollapsed RCD space, and is homeomorphic to the ...
Gabor Szekelyhidi
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Strict positivity of Kähler–Einstein currents
Forum of Mathematics, SigmaKähler–Einstein currents, also known as singular Kähler–Einstein metrics, have been introduced and constructed a little over a decade ago. These currents live on mildly singular compact Kähler spaces X and their two defining properties are the following:
Vincent Guedj +2 more
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Balanced Metrics and Noncommutative Kähler Geometry [PDF]
Symmetry, Integrability and Geometry: Methods and Applications, 2010 In this paper we show how Einstein metrics are naturally described using the quantization of the algebra of functions C^∞(M) on a Kähler manifold M. In this setup one interprets M as the phase space itself, equipped with the Poisson brackets inherited ...
Sergio Lukic
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Canonical metrics on generalized Hartogs triangles
Comptes Rendus. Mathématique, 2022 This paper is concerned with the canonical metrics on generalized Hartogs triangles. As main contributions, we first show the existence of a Kähler–Einstein metric on generalized Hartogs triangles.
Bi, Enchao, Hou, Zelin
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Pluricomplex Green's functions and Fano manifolds [PDF]
Épijournal de Géométrie Algébrique, 2019 We show that if a Fano manifold does not admit Kahler-Einstein metrics then the Kahler potentials along the continuity method subconverge to a function with analytic singularities along a subvariety which solves the homogeneous complex Monge-Ampere ...
Nicholas McCleerey, Valentino Tosatti
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Kähler–Einstein Metrics on Smooth Fano Symmetric Varieties with Picard Number One
Mathematics, 2021 Symmetric varieties are normal equivarient open embeddings of symmetric homogeneous spaces, and they are interesting examples of spherical varieties. We prove that all smooth Fano symmetric varieties with Picard number one admit Kähler–Einstein metrics ...
Jae-Hyouk Lee +2 more
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Smooth approximation of twisted Kähler-Einstein metrics
Advanced Nonlinear Studies, 2023 In this article, we prove the existence of smooth approximations of twisted Kähler-Einstein metrics using the variational method.
Jin Lize, Wang Feng
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K-stability of Fano varieties via admissible flags
Forum of Mathematics, Pi, 2022 We develop a general approach to prove K-stability of Fano varieties. The new theory is used to (a) prove the existence of Kähler-Einstein metrics on all smooth Fano hypersurfaces of Fano index two, (b) compute the stability thresholds for hypersurfaces ...
Hamid Abban, Ziquan Zhuang
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A polar dual to the momentum of toric Fano manifolds
Complex Manifolds, 2021 We introduce an invariant on the Fano polytope of a toric Fano manifold as a polar dual counterpart to the momentum of its polar dual polytope. Moreover, we prove that if the momentum of the polar dual polytope is equal to zero, then the dual invariant ...
Sano Yuji
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