A characteristicpanalogue of plt singularities and adjoint ideals

✍ Scribed by Shunsuke Takagi

• Publisher: Springer-Verlag
• Year: 2007
• Tongue: French
• Weight: 343 KB
• Volume: 259
• Category: Article
• ISSN: 0025-5874
• DOI: 10.1007/s00209-007-0227-z

✦ Synopsis

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.