Meromorphic maps of Kahler manifolds with trivial canonical bundles

2016/11/10 by Do Duc Thai, Thai, Do Duc, Duc-Viet Vu +2
Mathematics · #Complex Variables (math.CV) #FOS: Mathematics #Geometric Analysis and Curvature Flows #Geometry and complex manifolds #Meromorphic and Entire Functions #math.CV

paper · pdf · doi:10.48550/arxiv.1611.03373

This paper is an attempt to correct the mistake in our arXiv:1302.1107. However its proof is still wrong. So we would like to withdraw it

openalex publication_date 2016/11/10 · arxiv created 2017/11/10 · arxiv updated 2017/11/13 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

Let M be a (bounded or not) domain of Cⁿ which is complete with respect to a Kähler metric, or more generally, a complete Kähler manifold with trivial canonical bundle. Let f be a linearly nondegenerate meromorphic map from M to the complex projective space P^m. Under an assumption on the positivity of the pull-back by f of the Fubini-Study form on P^m, we prove that f can not omit a certain number of hyperplanes in subgeneral position in P^m. This is deduced directly from a non-integrated defect relation for such f which generalizes that obtained by Fujimoto in the case where M is a ball.

Citations

• Nevanlinna theory for meromorphic maps from a closed submanifold of ℂ^l to a compact complex manifold

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• Uniqueness problem of meromorphic mappings from a complete Kähler manifold into a projective variety
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