Singularities in arbitrary characteristic via jet schemes

Abstract

This paper summarizes the results at the present moment about singularities with respect to the Mather-Jacobian log discrepancies over algebraically closed field of arbitrary characteristic. The basic point is the Inversion of Adjunction with respect to Mather-Jacobian discrepancies holds in arbitrary characteristic. Based on this fact we will reduce many geometric properties of the singularities into the problem on jet schemes and try to avoid discussions which are distinctive for characteristic 0.

Typos are corrected. Some linguistic points are improved. Final version, to appear in " Hodge theory and L^2 analysis"

References in corpus (2)

• Singularities with respect to Mather-Jacobian discrepancies
• Log canonical thresholds in positive characteristic

Cited by in corpus (7)

• General hyperplane sections of threefolds in positive characteristic
• The minimal log discrepancies on a smooth surface in positive characteristic
• Finite determination conjecture for Mather-Jacobian minimal log discrepancies and its applications
• Computations of Mather Minimal Log Discrepancies
• Arc closures and the local isomorphism problem
• Inversion of modulo p reduction and a partial descent from characteristic 0 to positive characteristic
• On jet closures of singularities