Improvement of non-integrated defect relation for meromorphic maps from K\"{a}hler manifolds

TL;DR

This paper develops a new defect relation for meromorphic maps from Kähler manifolds to projective varieties, providing explicit bounds that are independent of the number of hypersurfaces involved, thus advancing complex geometry theory.

Contribution

It introduces a non-integrated defect relation with explicit truncation levels for meromorphic maps, independent of the number of hypersurfaces, generalizing previous results.

Findings

Established a defect relation with explicit truncation levels

Total defect and truncation level estimated independently of hypersurface count

Generalized and improved previous defect relation results

Abstract

The purpose of this paper is to establish a non-integrated defect relation for meromorphic mappings from a complete K\"{a}hler manifold into a projective variety intersecting an arbitrary family of hypersurfaces with explicit truncation level. In our result, both the total defect and the truncation level are estimated independently of the number of involving hypersurfaces. Our result generalizes and improves the previous results in this topic.