  We provide several results on splice-quotient singularities: a combinatorial
expression of the dimension of the first cohomology of all `natural' line
bundles, an equivariant Campillo-Delgado-Gusein-Zade type formula about the
dimension of relative sections of line bundles (proving that the equivariant,
divisorial multi-variable Hilbert series is topological), a combinatorial
description of divisors of analytic function-germs, and an expression for the
multiplicity of the singularity from its resolution graph.
  Additional, we establish a new formula for the Seiberg-Witten invariants of
any rational homology sphere singularity link.
