Metrics with cone singularities along normal crossing divisors and holomorphic tensor fields

Details Metrics with cone singularities along normal crossing divisors and holomorphic tensor fields Metrics with cone singularities along normal crossing divisors and holomorphic tensor fields

2011-04-26

arxiv.org/abs/1104.4879v2

Mathematics

Complex Variables

34 pages, v2: Title and abstract changed, exposition improved, more references, an error corrected in section 5.1

Scientific paper

We prove the existence of non-positively curved K\"ahler-Einstein metrics with cone singularities along a given simple normal crossing divisor of a compact K\"ahler manifold, under a technical condition on the cone angles. As an application we extend to this setting classical results of Lichnerowicz and Kobayashi on the parallelism and vanishing of appropriate holomorphic tensor fields.

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