Meromorphic maps of Kahler manifolds with trivial canonical bundles

Abstract

Let M be a (bounded or not) domain of C^n 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.

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

References in corpus (2)

• Non-integrated defect relation for meromorphic maps from a Kähler manifold intersecting hypersurfaces in subgeneral of ${\mathbb{P}}^n(\mathbb{C})$
• Holomorphic mappings into compact complex manifolds