Jet schemes of rational double point singularities

Abstract

We prove that for $m\in \mathbb{N},~m$ large enough, the number of irreducible components of the schemes of $m-$jets centered at a point which is a double point singularity is independent of $m$ and is equal to the number of exceptional curves on the minimal resolution of the singularity. We also relate some irreducible components of the jet schemes of an $E_6$ singularity to its "minimal" embedded resolutions of singularities.