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BY-NC-ND 4.0 license Open Access Published by De Gruyter Open Access March 22, 2017

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

  • Martin de Borbon
From the journal Complex Manifolds


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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Received: 2016-11-25
Accepted: 2017-2-28
Published Online: 2017-3-22
Published in Print: 2017-2-23

© 2017

This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 License.

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