Let X be a nonsingular variety (with dim X 2) over an algebraically closed field k of characteristic zero. Let α : Spec kJtK → X be an arc on X, and let v = ord α be the valuation given by the order of vanishing along α. We describe the maximal irreducible sub-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. As a corollary, we get that v is determined by its sequence of centers. Also, when X is a surface, our construction also applies to any divisorial valuation v, and in this case C (v) coincides with the one introduced in [L. Ein, R. Lazarsfeld, M. Musta¸tǎ, Contact loci in arc spaces,