
## 2. Singularities in char p

Questions about singularities of the MMP in characteristic p.
1. ### Terminal and Cohen-Macaulay

#### 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

#### 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.