Kahler-Einstein metric near an isolated log canonical singularity
arXiv:2106.05486
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.
arXiv commentCorrect the proof of Proposition 2.6 in pervious version
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- Riemannian geometry of Kahler-Einstein currents
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- Continuity of the Weil-Petersson potential
- On the construction of a complete Kahler-Einstein metric with negative scalar curvature near an isolated log-canonical singularity