2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/79467Locally analytically, any isolated double point occurs as a double covering of a smooth surface. It can be desingularized via the canonical resolution, as it is well-known. In this paper we explicitly compute the fundamental cycle of both the canonical and minimal resolution of a double point singularity and we classify those for which the fundamental cycle differs from the fiber cycle. Finally we compute the conditions that a double point imposes to pluricanonical systems.31 pages; partially rewrittenAlgebraic Geometry14J17; 32S25text