Jet schemes, log discrepancies and Inversion of Adjunction

Details Jet schemes, log discrepancies and Inversion of Adjunction Jet schemes, log discrepancies and Inversion of Adjunction

2002-09-27

arxiv.org/abs/math/0209392v3

Invent. Math. 153 (2003), 119-135.

Mathematics

Algebraic Geometry

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 bee

Scientific paper

10.1007/s00222-003-0298-3

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.

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