Singularities of Pairs via Jet Schemes

2001/02/26 by Mircea Mustata · 4 citations
Mathematics · #math.AG #msc:14B05 #msc:14E15

paper · pdf

published as J. Amer. Math. Soc. 15 (2002), 599-615. · 21 pages; LaTeX

arxiv created 2001/02/26 · arxiv updated 2009/11/30

Abstract

Let X be a smooth variety and Y a closed subscheme of X. By comparing motivic integrals on X and on a log resolution of (X,Y), we prove the following formula for the log canonical threshold of (X,Y): c(X,Y)=dim X-sup_m(dim Y_m/(m+1), where Y_m is the mth jet scheme of Y. We show how this formula can be used to study the log canonical threshold. In particular, we give a proof of the Semicontinuity theorem of Demailly and Kollár.

Cited by

• Jet Schemes, Newton Polygons and Continued Fractions
• On jet closures of singularities
• Liftings of ideals in positive characteristic to those in characteristic zero:Surface case
• On jet schemes of determinantal varieties

Related

• Log canonical thresholds in positive characteristic
• Singularities of log varieties via jet schemes
• Jet schemes and singularities
• Jet schemes of determinantal varieties
• Toward an inductive description of singularities of pairs