  The present work is a user's guide to the results of a previous paper by the
second and third authors, where a description of the space of characters of a
quasi-projective variety was given in terms of global quotient orbifold
pencils.
  Below we consider the case of plane curve complements and hyperplane
arrangements. In particular, an infinite family of curves exhibiting characters
of any torsion and depth~3 will be discussed. Also, in the context of line
arrangements, it will be shown how geometric tools, such as the existence of
orbifold pencils, can replace the group theoretical computations via
fundamental groups when studying characters of finite order, specially order
two. Finally, we revisit an Alexander-equivalent Zariski pair considered in the
literature and show how the existence of such pencils distinguishes both
curves.
