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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| Formato: | article |
| Lenguaje: | EN |
| Publicado: |
De Gruyter
2017
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| Acceso en línea: | https://doaj.org/article/0a574a81d34a4cd98d4233680c69365e |
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| Sumario: | 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. |
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