Defect relation of $n+1$ components through the GCD method]

TL;DR

This paper advances the understanding of defect relations in complex analysis by extending existing results to moving targets and analyzing degeneracy loci using the GCD method.

Contribution

It extends the defect relation results to moving targets and provides an effective way to determine degeneracy loci independent of the maps.

Findings

Extended defect relation to moving targets.

Studied truncated defect relations.

Determined degeneracy loci effectively.

Abstract

This paper studies the defect relation through the GCD method. In particular, among other results, we extend the defect relation result of Chen, Huynh, Sun and Xie to moving targets. The truncated defect relation is also studied. Furthermore, we obtain the degeneracy locus, which can be determined effectively and is independent of the maps under the consideration.