Singularities of log varieties via jet schemes

TL;DR

This paper extends the understanding of singularities in log varieties by analyzing their jet schemes, establishing a criterion for canonical singularities based on the irreducibility of log jet schemes.

Contribution

It generalizes Mustata's theorem from ordinary to logarithmic jet schemes, providing a new criterion for canonical singularities in log varieties.

Findings

Log jet schemes of a normal local complete intersection log variety are irreducible if and only if the variety has canonical singularities.

Generalization of Mustata's theorem to the logarithmic setting.

Establishment of a link between jet scheme irreducibility and singularity type in log varieties.

Abstract

We study logarithmic jet schemes of a log scheme and generalize a theorem of M. Mustata from the case of ordinary jet schemes to the logarithmic case. If X is a normal local complete intersection log variety, then X has canonical singularities if and only if the log jet schemes of X are irreducible.