  We study loci of arcs on a smooth variety defined by order of contact with a
fixed subscheme. Specifically, we establish a Nash-type correspondence showing
that the irreducible components of these loci arise from (intersections of)
exceptional divisors in a resolution of singularities. We show also that these
loci account for all the valuations determined by irreducible cylinders in the
arc space. Along the way, we recover in an elementary fashion-without using
motivic integration-results of the third author relating singularities to arc
spaces. Moreover, we extend these results to give a jet-theoretic
interpretation of multiplier ideals.
