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

Martin de Borbon. "Singularities of plane complex curves and limits of Kähler metrics with cone singularities. I: Tangent Cones." Complex Manifolds 4.1 (2017): 43-72. <http://eudml.org/doc/288032>.

@article{MartindeBorbon2017,
abstract = {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.},
author = {Martin de Borbon},
journal = {Complex Manifolds},
keywords = {Kähler-Einstein metrics with cone singularities; Gromov-Hausdorff limits; Tangent cones},
language = {eng},
number = {1},
pages = {43-72},
title = {Singularities of plane complex curves and limits of Kähler metrics with cone singularities. I: Tangent Cones},
url = {http://eudml.org/doc/288032},
volume = {4},
year = {2017},
}

TY - JOUR
AU - Martin de Borbon
TI - Singularities of plane complex curves and limits of Kähler metrics with cone singularities. I: Tangent Cones
JO - Complex Manifolds
PY - 2017
VL - 4
IS - 1
SP - 43
EP - 72
AB - 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.
LA - eng
KW - Kähler-Einstein metrics with cone singularities; Gromov-Hausdorff limits; Tangent cones
UR - http://eudml.org/doc/288032
ER -