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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.
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 -