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

Aijin Lin; Liangming Shen

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

Differential Geometry 2018-03-22 v2

Authors: Aijin Lin , Liangming Shen

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.

Keywords

K\"{a}hler-Einstein metric Fano manifold simple normal crossing divisor conic metric curvature estimate holomorphic vector field cone angle

Cite

@article{arxiv.1603.06329,
  title  = {Conic K\"{a}hler-Einstein metrics along simple normal crossing divisors on Fano manifolds},
  author = {Aijin Lin and Liangming Shen},
  journal= {arXiv preprint arXiv:1603.06329},
  year   = {2018}
}

Comments

arXiv admin note: text overlap with arXiv:1511.00183. Accepted by J. Func. Anal

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

Abstract

Keywords

Cite

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