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What is an example of a Fano variety of Picard number 1 that does not have log-canonical singularities?

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    $\begingroup$ Are singular hypersurfaces of low degree log-canonical? Because they are Fano with Picard number one... $\endgroup$
    – Piotr Achinger
    Commented Mar 21, 2012 at 17:57
  • $\begingroup$ Piotr, they don't need to be log canonical I don't think. Log canonical is basically a local version of Frobenius split. In other words, if you have a variety that is not locally Frobenius split for any p, then it is not log canonical either (at least up to some big conjectures). $\endgroup$
    – Karl Schwede
    Commented Mar 21, 2012 at 20:37

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