Let $X$ be a generic determinantal affine variety over a perfect field of characteristic $p \geq 0$ and $P \subset X$ be a standard prime divisor generator of $\mathrm{ Cl}(X) \cong \mathbb{ Z}$. We prove that the pair $(X,P)$ is purely $F$-regular if $p>0$ and so that $(X,P)$ is purely log terminal (PLT) if $p=0$ and $(X,P)$ is log $\mathbb{ Q}$-Gorenstein. In general, using recent results of Z. Zhuang and S. Lyu, we show that $(X,P)$ is of PLT-type, i.e. there is a $\mathbb{ Q}$-divisor $\Delta$ with coefficients in $[0,1)$ such that $(X,P+\Delta)$ is PLT.
Categories: math.AG math.AC