Nash blow-ups of jet schemes

TL;DR

This paper explores the construction of relative compactifications of maps on jet schemes, especially focusing on Nash blow-ups, providing explicit methods and revealing their structure.

Contribution

It introduces a natural, explicit construction of relative compactifications for maps on jet schemes, linking Nash blow-ups with jet scheme components.

Findings

Relative compactifications are explicitly constructed for jet scheme maps.

Nash blow-ups of a variety induce Nash blow-ups on jet scheme components.

The method clarifies the structure of jet schemes under Nash blow-ups.

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.