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arXiv · 1104.4879

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

Frédéric Campana·Henri Guenancia·Mihai Păun
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Abstract

We prove the existence of non-positively curved K\"ahler-Einstein metrics with cone singularities along a given simple normal crossing divisor on a compact K\"ahler manifold, under a technical condition on the cone angles, and we also discuss the case of positively-curved K\"ahler-Einstein metrics with cone singularities. 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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Frédéric Campana, Henri Guenancia, Mihai Păun. 2011-04-26. Metrics with cone singularities along normal crossing divisors and holomorphic tensor fields. https://arxiv.org/abs/1104.4879

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