  This note is based on a talk given at the 2019 ISAAC Congress in Aveiro,
Portugal. We give an expository account of joint work with Daniele Alessandrini
and Gye-Seon Lee on Hitchin components for orbifold groups (arXiv:1811.05366),
recasting part of it in the language of analytic orbi-curves. This reduces the
computation of the dimension of the Hitchin component for orbifold groups to an
application of the orbifold Riemann-Roch theorem.
