Lawrence Ein, Mircea Mustata, Takehiko Yasuda
Published 2002-09-27, updated 2003-02-22Version 3
We use the theory of motivic integration for singular spaces to give a characterization of minimal log discrepencies in terms of the codimension of certain subsets of spaces of arcs. This is done for arbitrary pairs $(X,Y)$, with $X$ normal and Q-Gorenstein. As a first application, we prove a precise version of Inversion of Adjunction, in the case when the ambient variety is smooth. Another application concerns the semicontinuity of minimal log discrepancies on smooth varieties.
Comments: 17 pages, AMS-LaTeX; v.2: the statement of Corollary 2.4 is corrected, Theorems 2.5 and 2.6 from the previous version have been combined in one stronger statement; v.3: final version, to appear in Invent. Math
Journal: Invent. Math. 153 (2003), 119-135.
Jet schemes and singularities
On a comparison of minimal log discrepancies in terms of motivic integration
A counterexample to the PIA conjecture for minimal log discrepancies
![QR code for arXiv:math/0209392 [math.AG]](http://oss.arxitics.com/images/favicon.svg)