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An interpretation of multiplier ideals via tight closure. (English) Zbl 1080.14004

N. Hara [Trans. Am. Math. Soc. 353, 1885–1906 (2001; Zbl 0976.13003)] and K. Smith [Commun. Algebra 28, 5915–5929 (2000; Zbl 0979.13007)] 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. In the paper under review the author extends this result for a pair \((R,\Delta)\) of a normal ring \(R\) and an effective \(\mathbb{Q}\)-Weil divisor \(\Delta\) on \({\text{Spec}}\,R\). As a corollary, he obtains the equivalence of strongly \({\text{F}}\)-regular pairs and pairs.

MSC:

14B05 Singularities in algebraic geometry
13A35 Characteristic \(p\) methods (Frobenius endomorphism) and reduction to characteristic \(p\); tight closure
14E30 Minimal model program (Mori theory, extremal rays)
14C20 Divisors, linear systems, invertible sheaves
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References:

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