An interpretation of multiplier ideals via tight closure
Author:
Shunsuke Takagi
Journal:
J. Algebraic Geom. 13 (2004), 393415
DOI:
https://doi.org/10.1090/S1056391103003667
Published electronically:
December 4, 2003
MathSciNet review:
2047704
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Abstract  References  Additional Information
Abstract: Hara [Trans. Amer. Math. Soc. 353 (2001), 1885–1906] and Smith [Comm. Algebra 28 (2000), 5915–5929] independently proved that in a normal ${\mathbb Q}$Gorenstein ring of characteristic $p \gg 0$, the test ideal coincides with the multiplier ideal associated to the trivial divisor. We extend this result for a pair $(R, \Delta )$ of a normal ring $R$ and an effective ${\mathbb Q}$Weil divisor $\Delta$ on $\operatorname {Spec}R$. As a corollary, we obtain the equivalence of strongly $\text {F}$regular pairs and $\text {klt}$ pairs.

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Additional Information
Shunsuke Takagi
Affiliation:
Graduate School of Mathematical Sciences, University of Tokyo, 381, Komaba, Meguro, Tokyo 1538914, Japan
Email:
stakagi@ms.utokyo.ac.jp
Received by editor(s):
December 17, 2001
Published electronically:
December 4, 2003