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Complex Manifolds

Ed. by Fino, Anna Maria

CiteScore 2017: 0.39

SCImago Journal Rank (SJR) 2017: 0.260
Source Normalized Impact per Paper (SNIP) 2017: 0.660

Mathematical Citation Quotient (MCQ) 2017: 0.18

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

Martin de Borbon
Published Online: 2017-03-22 | DOI: https://doi.org/10.1515/coma-2017-0005


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.

Keywords : Kähler-Einstein metrics with cone singularities; Gromov-Hausdorff limits; Tangent cones


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About the article

Received: 2016-11-25

Accepted: 2017-02-28

Published Online: 2017-03-22

Published in Print: 2017-02-23

Citation Information: Complex Manifolds, Volume 4, Issue 1, Pages 43–72, ISSN (Online) 2300-7443, DOI: https://doi.org/10.1515/coma-2017-0005.

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© 2017. This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 License. BY-NC-ND 4.0

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