Jet schemes of homogeneous hypersurfaces

TL;DR

This paper investigates the singularities of jet schemes of homogeneous hypersurfaces, establishing conditions under which these jet schemes exhibit dense F-regularity and rational singularities across all levels.

Contribution

It provides new criteria linking degree and dimension to the singularity types of jet schemes of homogeneous hypersurfaces, with explicit examples.

Findings

Jet schemes can have dense F-regular singularities under specific degree and dimension conditions.

Examples of singular varieties with jet schemes possessing rational singularities for all levels.

Conditions for the singularities of jet schemes to be of dense F-regular type.

Abstract

This paper studies the singularities of jet schemes of homogeneous hypersurfaces of general type. We obtain the condition of the degree and the dimension for the singularities of the jet schemes to be of dense $F$-regular type. This provides us with examples of singular varieties whose $m$-jet schemes have rational singularities for every $m$.