Meromorphic mappings into projective varieties with arbitrary families of moving hypersurfaces

Abstract

In this paper, we prove a general second main theorem for meromorphic mappings into a subvariety $V$ of ${\mathbb{P}}^N(\mathbb{C})$ with an arbitrary family of moving hypersurfaces. Our second main theorem generalizes and improves all previous results for meromorphic mappings with moving hypersurfaces, in particular for meromorphic mappings and families of moving hypersurfaces in subgeneral position. The method of our proof is different from that of previous authors used for the case of moving hypersurfaces.

In this version, some mistakes have been corrected. The current version has 25 pages. This paper has been accepted for publication in The Journal of Geometric Analysis (2021). arXiv admin note: text overlap with arXiv:2012.07204

References in corpus (1)

• Generalizations of degeneracy second main theorem and Schmidt's subspace theorem

Cited by in corpus (3)

• Holomorphic maps from complex discs intersecting families of hypersurfaces
• Defect relation for holomorphic maps from complex discs into projective varieties and hypersurfaces
• Improvement of non-integrated defect relation for meromorphic maps from Kähler manifolds