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Singularities of pairs via jet schemes


Author: Mircea Mustaţǎ
Journal: J. Amer. Math. Soc. 15 (2002), 599-615
MSC (2000): Primary 14B05; Secondary 14B10, 14E30
DOI: https://doi.org/10.1090/S0894-0347-02-00391-0
Published electronically: February 14, 2002
MathSciNet review: 1896234
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Abstract: Let $X$ be a smooth variety and $Y\subset X$ a closed subscheme. We use motivic integration on the space of arcs of $X$ to characterize the fact that $(X,Y)$ is log canonical or log terminal using the dimension of the jet schemes of $Y$. This gives a formula for the log canonical threshold of $(X,Y)$, which we use to prove a result of Demailly and Kollár on the semicontinuity of log canonical thresholds.


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Additional Information

Mircea Mustaţǎ
Affiliation: Department of Mathematics, University of California, Berkeley, California 94720 – and – Institute of Mathematics of the Romanian Academy
Address at time of publication: Clay Mathematics Institute, 1770 Massachusetts Avenue, No. 331, Cambridge, Massachusetts 02140
Email: mirceamustata@yahoo.com

Keywords: Jet schemes, log canonical threshold, motivic integration
Received by editor(s): March 2, 2001
Published electronically: February 14, 2002
Article copyright: © Copyright 2002 American Mathematical Society