2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/172204We 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.16 pagesAlgebraic Geometry32S05; 32S25; 57M27; 32S45; 32S50; 32C35; 57R57;text