Author： Takagi Shunsuke
Publisher： Springer Publishing Company
ISSN： 0025-5874
Source： Mathematische Zeitschrift, Vol.259, Iss.2, 2008-06, pp. : 321-341
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Abstract
We introduce a new variant of tight closure and give an interpretation of adjoint ideals via this tight closure. As a corollary, we prove that a log pair (X, Δ) is plt if and only if the modulo p reduction of (X, Δ) is divisorially F-regular for all large p ≫ 0. Here, divisorially F-regular pairs are a class of singularities in positive characteristic introduced by Hara and Watanabe (J Algebra Geom 11:363–392, 2002) in terms of Frobenius splitting.
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