  Locally 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.
