arXiv math/06034602006-03math.AGmath.AC

A characteristic p analogue of plt singularities and adjoint ideals

Shunsuke Takagi

备注：: 22 pages. A lot of changes. Some errors and many typos fixed

英文摘要：

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 $p \gg 0$. Here, divisorially F-regular pairs are a class of singularities in positive characteristic introduced by Hara and Watanabe in terms of Frobenius splitting.

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