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

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 elementa...

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Autor principal:	Borbon Martin de
Formato:	article
Lenguaje:	EN
Publicado:	De Gruyter 2017
Materias:	kähler-einstein metrics with cone singularities gromov-hausdorff limits tangent cones Mathematics QA1-939
Acceso en línea:	https://doaj.org/article/0a574a81d34a4cd98d4233680c69365e
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spelling	oai:doaj.org-article:0a574a81d34a4cd98d4233680c69365e2021-12-02T17:14:47ZSingularities of plane complex curves and limits of Kähler metrics with cone singularities. I: Tangent Cones2300-744310.1515/coma-2017-0005https://doaj.org/article/0a574a81d34a4cd98d4233680c69365e2017-02-01T00:00:00Zhttps://doi.org/10.1515/coma-2017-0005https://doaj.org/toc/2300-7443The 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 construction with respect to the S1-action generated by the Reeb vector field, except in the irregular case ℂβ₁×ℂβ₂ with β₂/ β₁ ∉ Q.Borbon Martin deDe Gruyterarticlekähler-einstein metrics with cone singularitiesgromov-hausdorff limitstangent conesMathematicsQA1-939ENComplex Manifolds, Vol 4, Iss 1, Pp 43-72 (2017)
institution	DOAJ
collection	DOAJ
language	EN
topic	kähler-einstein metrics with cone singularities gromov-hausdorff limits tangent cones Mathematics QA1-939
spellingShingle	kähler-einstein metrics with cone singularities gromov-hausdorff limits tangent cones Mathematics QA1-939 Borbon Martin de Singularities of plane complex curves and limits of Kähler metrics with cone singularities. I: Tangent Cones
description	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 construction with respect to the S1-action generated by the Reeb vector field, except in the irregular case ℂβ₁×ℂβ₂ with β₂/ β₁ ∉ Q.
format	article
author	Borbon Martin de
author_facet	Borbon Martin de
author_sort	Borbon Martin de
title	Singularities of plane complex curves and limits of Kähler metrics with cone singularities. I: Tangent Cones
title_short	Singularities of plane complex curves and limits of Kähler metrics with cone singularities. I: Tangent Cones
title_full	Singularities of plane complex curves and limits of Kähler metrics with cone singularities. I: Tangent Cones
title_fullStr	Singularities of plane complex curves and limits of Kähler metrics with cone singularities. I: Tangent Cones
title_full_unstemmed	Singularities of plane complex curves and limits of Kähler metrics with cone singularities. I: Tangent Cones
title_sort	singularities of plane complex curves and limits of kähler metrics with cone singularities. i: tangent cones
publisher	De Gruyter
publishDate	2017
url	https://doaj.org/article/0a574a81d34a4cd98d4233680c69365e
work_keys_str_mv	AT borbonmartinde singularitiesofplanecomplexcurvesandlimitsofkahlermetricswithconesingularitiesitangentcones
_version_	1718381242627391488

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

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