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Local classification of chsc Kähler metrics with cone singularities
Abstract
Let B⊂ℂn be a ball centred at the origin and D={z1=0}. Let g be a Kähler metric of constant holomorphic sectional curvature (chsc) on B∖ D, uniformly equivalent to the model cone metric of angle 2πβ, with 0<β<1, and polyhomogeneous along D. We prove that, in suitable holomorphic coordinates (w1, …, wn) centred at the origin, the metric g is the pullback of the corresponding complex space form by the map (w1,w2,…,wn)longmapsto ((w1)β,w2,…,wn).
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BibTeX
@misc{borbon2026local,
title = {{Local classification of chsc Kähler metrics with cone singularities}},
author = {Martin de Borbon},
howpublished = {arXiv},
year = {2026},
month = sep,
doi = {10.48550/arxiv.2609.11760},
eprint = {2609.11760},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2609.11760},
}
RIS
TY - UNPB
TI - Local classification of chsc Kähler metrics with cone singularities
AU - Martin de Borbon
PY - 2026
DA - 2026/09/10
PB - arXiv
DO - 10.48550/arxiv.2609.11760
UR - https://arxiv.org/abs/2609.11760
AB - Let B⊂ℂ^n be a ball centred at the origin and D={z^1=0}. Let g be a Kähler metric of constant holomorphic sectional curvature (chsc) on B∖ D, uniformly equivalent to the model cone metric of angle 2πβ, with 0<β<1, and polyhomogeneous along D. We prove that, in suitable holomorphic coordinates (w^1, …, w^n) centred at the origin, the metric g is the pullback of the corresponding complex space form by the map (w^1,w^2,…,w^n)longmapsto ((w^1)^β,w^2,…,w^n).
ER -