Versal Deformations of Formal Arcs *

Let X be a complex algebraic variety, and X◦ ⊂ X be the smooth part of X. Consider the scheme L(X) of formal arcs in X. The C-points of L(X) are just maps D = SpecC[[t]] → X (see, for example, [DL] for a definition of L(X) as a scheme). Let L◦(X) be the open subscheme of arcs whose image is not contained in X \X◦. Fix an arc γ : D → X in L◦(X), and let L(X)γ be the formal neighborhood of γ in L(X). The purpose of this paper is to prove the following.