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arXiv · 2106.05486

Kahler-Einstein metric near an isolated log canonical singularity

Ved Datar·Xin Fu·Jian Song
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Abstract

We construct Kahler-Einstein metrics with negative scalar curvature near an isolated log canonical (non-log terminal) singularity. Such metrics are complete near the singularity if the underlying space has complex dimension 2 or if the singularity is smoothable. In complex dimension 2, we show that any complete Kahler-Einstein metric of negative scalar curvature near an isolated log canonical (non-log terminal) singularity is smoothly asymptotically close to one of the model metrics constructed by Kobayashi and Nakamura arising from hyperbolic geometry.

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Ved Datar, Xin Fu, Jian Song. 2021-06-10. Kahler-Einstein metric near an isolated log canonical singularity. https://arxiv.org/abs/2106.05486

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