We describe a notion of ampleness for line bundles on orbifolds with cyclic quotient singularities that is related to embeddings in weighted projective space, and prove a global asymptotic expansion for a weighted Bergman kernel associated to such a line bundle.
"Weighted Bergman Kernels on Orbifolds." J. Differential Geom. 88 (1) 87 - 107, May 2011. https://doi.org/10.4310/jdg/1317758870