English

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 (X,Y)(X,Y), with XX 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.

Keywords

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

R2 v1 2026-07-22T16:48:00.142Z