Displaying similar documents to “Metrics with cone singularities along normal crossing divisors and holomorphic tensor fields”

Singularities of plane complex curves and limits of Kähler metrics with cone singularities. I: Tangent Cones

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...

An extension theorem for Kähler currents with analytic singularities

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.

Kähler-Einstein metrics: Old and New

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.

Toric extremal Kähler-Ricci solitons are Kähler-Einstein

Simone Calamai, David Petrecca (2017)

Complex Manifolds

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In this short note, we prove that a Calabi extremal Kähler-Ricci soliton on a compact toric Kähler manifold is Einstein. This settles for the class of toric manifolds a general problem stated by the authors that they solved only under some curvature assumptions.