Jet schemes, log discrepancies and Inversion of Adjunction
Algebraic Geometry
2009-11-07 v3
Abstract
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 , with 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.
Cite
@article{arxiv.math/0209392,
title = {Jet schemes, log discrepancies and Inversion of Adjunction},
author = {Lawrence Ein and Mircea Mustata and Takehiko Yasuda},
journal= {arXiv preprint arXiv:math/0209392},
year = {2009}
}
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