Article contents
On the
$F$-purity of isolated log canonical singularities
Published online by Cambridge University Press: 20 June 2013
Abstract
A singularity in characteristic zero is said to be of dense $F$-pure type if its modulo
$p$ reduction is locally Frobenius split for infinitely many
$p$. We prove that if
$x\in X$ is an isolated log canonical singularity with
$\mu (x\in X)\leq 2$ (where the invariant
$\mu $ is as defined in Definition 1.4), then it is of dense
$F$-pure type. As a corollary, we prove the equivalence of log canonicity and being of dense
$F$-pure type in the case of three-dimensional isolated
$ \mathbb{Q} $-Gorenstein normal singularities.
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- Research Article
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- Copyright
- © The Author(s) 2013
References
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