## 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

### Citations:

Zbl 0976.13003; Zbl 0979.13007
Full Text:

### References:

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