Remarks on the Existence Problem of Positive Kähler-Einstein Metrics.
Wei-Yue Ding (1988)
Mathematische Annalen
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Wei-Yue Ding (1988)
Mathematische Annalen
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P. Topiwala (1987)
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Claude LeBrun (1991)
Journal für die reine und angewandte Mathematik
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Tristan C. Collins, Valentino Tosatti (2014)
Annales de la faculté des sciences de Toulouse Mathématiques
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We prove an extension theorem for Kähler currents with analytic singularities in a Kähler class on a complex submanifold of a compact Kähler manifold.
Frédéric Campana, Henri Guenancia, Mihai Păun (2013)
Annales scientifiques de l'École Normale Supérieure
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We prove the existence of non-positively curved Kähler-Einstein metrics with cone singularities along a given simple normal crossing divisor of a compact Kähler manifold, under a technical condition on the cone angles, and we also discuss the case of positively-curved Kähler-Einstein metrics with cone singularities. As an application we extend to this setting classical results of Lichnerowicz and Kobayashi on the parallelism and vanishing of appropriate holomorphic tensor fields. ...
Jean Varouchas (1989)
Mathematische Annalen
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P. Topiwala (1987)
Inventiones mathematicae
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Claude LeBrun, Michael Singer (1993)
Inventiones mathematicae
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Yann Rollin, Michael Singer (2009)
Journal of the European Mathematical Society
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G. Tian (1987)
Inventiones mathematicae
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Daniele Angella, Cristiano Spotti (2017)
Complex Manifolds
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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.
Huai-Dong Cao (1985)
Inventiones mathematicae
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Andrew Swann (1991)
Mathematische Annalen
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Martin de Borbon (2017)
Complex Manifolds
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The goal of this article is to provide a construction and classification, in the case of two complex dimensions, of the possible tangent cones at points of limit spaces of non-collapsed sequences of Kähler-Einstein metrics with cone singularities. The proofs and constructions are completely elementary, nevertheless they have an intrinsic beauty. In a few words; tangent cones correspond to spherical metrics with cone singularities in the projective line by means of the Kähler quotient...