Conic K\"{a}hler-Einstein metrics along simple normal crossing divisors on Fano manifolds

Aijin Lin; Liangming Shen

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arXiv · 1603.06329

Conic K\"{a}hler-Einstein metrics along simple normal crossing divisors on Fano manifolds

Aijin Lin·Liangming Shen

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Abstract

We prove that on one K\"{a}hler-Einstein Fano manifold without holomorphic vector fields, there exists a unique conical K\"{a}hler-Einstein metric along a simple normal crossing divisor with admissible prescribed cone angles. We also establish a curvature estimate for conic metrics along a simple normal crossing divisor which generalizes Li-Rubinstein's estimate and derive high order estimates from this estimate.

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BibTeX RIS

Aijin Lin, Liangming Shen. 2016-03-21. Conic K\"{a}hler-Einstein metrics along simple normal crossing divisors on Fano manifolds. https://arxiv.org/abs/1603.06329

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