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Journal of Algebraic Geometry

Journal of Algebraic Geometry

Online ISSN 1534-7486; Print ISSN 1056-3911



An interpretation of multiplier ideals via tight closure

Author: Shunsuke Takagi
Journal: J. Algebraic Geom. 13 (2004), 393-415
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, 3-8-1, Komaba, Meguro, Tokyo 153-8914, Japan

Received by editor(s): December 17, 2001
Published electronically: December 4, 2003