Singularities in arbitrary characteristic via jet schemes

2015/10/18 by Shihoko Ishii, Ishii, Shihoko, Ana J. Reguera +1 · 2 citations
Mathematics · Physics and Astronomy · #14B05 #14H20 #Advanced Differential Equations and Dynamical Systems #Algebraic Geometry (math.AG) #Algebraic Geometry and Number Theory #FOS: Mathematics #Nonlinear Waves and Solitons

paper · pdf · doi:10.48550/arxiv.1510.05210

openalex publication_date 2015/10/18 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

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.

Cited by

• On jet closures of singularities
• Liftings of ideals in positive characteristic to those in characteristic zero:Surface case

Related

• Finite determination conjecture for Mather-Jacobian minimal log discrepancies and its applications
• Jet schemes and singularities
• Singularities of log varieties via jet schemes
• Smoothness and jet schemes
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