  Let X be a complex analytic space. A short analytic arc is a holomorphic map
of the closed unit disc to X such that only the origin is mapped to a singular
point. In contrast with the space of formal arcs studied by Nash, the moduli
space of short analytic arcs usually has infinitely many connected components.
We describe these for surface singularities, in terms of certain conjugacy
classes of the fundamental group of the link.
  For quotient singularities (in any dimension), this gives a concrete
realization of the McKay correspondence. Our results also give new connections
between a surface cusp singularity, its dual and hyperbolic Inoue surfaces.
version 2: References added.
