Log canonical thresholds in positive characteristic

Abstract

In this paper, we study the singularities of a pair (X,Y) in arbitrary characteristic via jet schemes. For a smooth variety X in characteristic 0, Ein, Lazarsfeld and Mustata showed that there is a correspondence between irreducible closed cylinders and divisorial valuations on X. Via this correspondence, one can relate the codimension of a cylinder to the log discrepancy of the corresponding divisorial valuation. We now extend this result to positive characteristic. In particular, we prove Mustata's log canonical threshold formula avoiding the use of log resolutions, making the formula available also in positive characteristic. As a consequence, we get a comparison theorem via reduction modulo p and a version of Inversion of Adjunction in positive characteristic.

19 pages

References in corpus (1)

• Contact loci in arc spaces

Cited by in corpus (5)

• Singularities in arbitrary characteristic via jet schemes
• On the behavior of singularities at the $F$-pure threshold
• The dimension of jet schemes of singular varieties
• Finite determination conjecture for Mather-Jacobian minimal log discrepancies and its applications
• Inversion of modulo p reduction and a partial descent from characteristic 0 to positive characteristic