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2. Singularities in char p

Questions about singularities of the MMP in characteristic p.

    1. Terminal and Cohen-Macaulay


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      Problem 2.1.

      [Kollár] Are (log) terminal singularities Cohen-Macaulay? Rational?
          This is affirmative in dimension two by the classification, but even the three-dimensional case seems interesting. One possible example: take the cone over a smooth Fano which admits a counterexample to Kodaira vanishing. One such exists in dimension 6(?), and should be log terminal but not Cohen-Macaulay.

        • Normality of plt pairs


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          Problem 2.2.

          [Hacon] Suppose that $(X,D = S+B)$ is a plt pair. Must $S$ be normal?
              If this isn’t true, there may be an obstruction to existence of flips.

              Cite this as: AimPL: The minimal model program in characteristic p, available at http://aimpl.org/minimalmodcharp.