Geodesic
Singularities of pairs via jet schemes
Mustaţǎ, Mircea1, 2
1Department of Mathematics, University of California, Berkeley, California 94720 – and – Institute of Mathematics of the Romanian Academy
2Clay Mathematics Institute, 1770 Massachusetts Avenue, No. 331, Cambridge, Massachusetts 02140
Journal of the American Mathematical Society, Tome 15 (2002) no. 3, pp. 599-615
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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.
DOI : 10.1090/S0894-0347-02-00391-0

Mustaţǎ, Mircea  1 , 2

1 Department of Mathematics, University of California, Berkeley, California 94720 – and – Institute of Mathematics of the Romanian Academy
2 Clay Mathematics Institute, 1770 Massachusetts Avenue, No. 331, Cambridge, Massachusetts 02140 
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Mustaţǎ, Mircea. Singularities of pairs via jet schemes. Journal of the American Mathematical Society, Tome 15 (2002) no. 3, pp. 599-615. doi: 10.1090/S0894-0347-02-00391-0

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