  For a normalized transcendence degree zero arc valuation v on a nonsingular
variety X (with dim X > 1), we describe the maximal irreducible subset C(v) of
the arc space of X such that the valuation given by the order of vanishing
along a general arc of C(v) equals v. We describe C(v) both algebraically, in
terms of the sequence of valuation ideals of v, and geometrically, in terms of
the sequence of infinitely near points associated to v. When X is a surface,
our construction also applies to any divisorial valuation v, and in this case
C(v) coincides with a subset Ein, Lazarsfeld, and Mustata associate to v.
