Non-integrated defect relation for meromorphic mappings from a Kähler manifold with hypersurfaces of a projective variety in subgeneral position

2017/12/14 by Si Duc Quang, Quang, Si Duc, Le Ngoc Quynh +3
Mathematics · #32A22 #Complex Variables (math.CV) #FOS: Mathematics #Primary 32H30 #Secondary 30D35 #math.CV #msc:30D35 #msc:32A22 #msc:32H30

paper · pdf · doi:10.48550/arxiv.1712.05698

The order of the name and affiliation of the second author have been changed. The paper is accepted for publication in Tohoku Journal of Mathematics, Vol 72, no. 2 (June 2021). arXiv admin note: substantial text overlap with arXiv:1610.08390

arxiv created 2020/10/06 · arxiv updated 2020/10/08

Abstract

In this paper, we establish a truncated non-integrated defect relation for meromorphic mappings from a complete Kähler manifold into a projective variety intersecting a family of hypersurfaces located in subgeneral position, where the truncation level of the defect is explicitly estimated. Our result generalizes and improves previous ones. In particular, when the family of hypersurfaces located in general position, our theorem will implies the previous result of Min Ru-Sogome. In the last part of this paper we will apply ours to study the distribution of the Gauss map of minimal surfaces.

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