## Singularities of pairs via jet schemes

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- by Mircea Mustaţǎ
- J. Amer. Math. Soc.
**15**(2002), 599-615 - DOI: https://doi.org/10.1090/S0894-0347-02-00391-0
- Published electronically: February 14, 2002
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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.## References

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## Bibliographic 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
- Received by editor(s): March 2, 2001
- Published electronically: February 14, 2002
- © Copyright 2002 American Mathematical Society
- 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
- MathSciNet review: 1896234