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On the
$F$-purity of isolated log canonical singularities
- Part of
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- Journal:
- Compositio Mathematica / Volume 149 / Issue 9 / September 2013
- Published online by Cambridge University Press:
- 20 June 2013, pp. 1495-1510
- Print publication:
- September 2013
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- Article
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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.
