Nash blow-ups of jet schemes

Abstract

Given an arbitrary projective birational morphism of varieties, we provide a natural and explicit way of constructing relative compactifications of the maps induced on the main components of the jet schemes. In the case the morphism is the Nash blow-up of a variety, such relative compactifications are shown to be given by the Nash blow-ups of the main components of the jet schemes.

Lemma 2.4 was incorrect and has been removed, and the proof of Lemma 2.1 has been adjusted; to appear in Ann. Inst. Fourier