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.
@article{bwmeta1.element.doi-10_1515_coma-2017-0005,
author = {Martin de Borbon},
title = {Singularities of plane complex curves and limits of K\"ahler metrics with cone singularities. I: Tangent Cones},
journal = {Complex Manifolds},
volume = {4},
year = {2017},
pages = {43-72},
language = {en},
url = {http://dml.mathdoc.fr/item/bwmeta1.element.doi-10_1515_coma-2017-0005}
}
Martin de Borbon. Singularities of plane complex curves and limits of Kähler metrics with cone singularities. I: Tangent Cones. Complex Manifolds, Tome 4 (2017) pp. 43-72. http://gdmltest.u-ga.fr/item/bwmeta1.element.doi-10_1515_coma-2017-0005/