Torsion divisors of plane curves and Zariski pairs

This paper is devoted to the study of the embedded topology of reducible plane curves having a smooth irreducible component. In previous studies, the relationship between the topology and certain torsion classes in the Picard group of degree zero of the smooth component was implicitly considered. Here this relationship is formulated clearly and a criterion is given for distinguishing the embedded topology in terms of torsion classes. Furthermore, a method is presented for systematically constructing examples of curves where this criterion is applicable, and new examples of Zariski $N$-tuples are produced.