Nash's conjecture on arcs and exceptional curves of surface singularities

Let $(S,s)$ be an isolated surface singularity, let $(X_0,\{E_\alpha\}_{(\alpha)})\longrightarrow(S,s)$ be a resolution of singularities, and let $\mathcal{H}$ be the infinite-dimensional algebraic variety of arcs on the singular germ. The minimal resolution is the resolution whose exceptional curves are minimal in the usual sense.

Nash's conjecture. The number of exceptional curves in the minimal resolution of $(S,s)$ equals the number of irreducible components of $\mathcal{H}$.

This conjecture compares the irreducible components of the space of formal arcs through the singularity with the exceptional components of a resolution. The source states it for surface singularities; its resolution status is not specified in the supplied text.