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I am looking for an example of a normal affine variety $V$ over a perfect field $k$ such that the differentials $\Omega_{V/k}$ are not torsion free. If normality is not required, an example is given by the Whitney umbrella in characteristic $2$: $V = V(x^2 - y z^2)$. On V we have

$0 = d(x^2 - y z^2) = 2xdx - z^2dy - 2yzdz = -z^2dy$.

So $dy$ is torsion as it is annihilated by $z^2$.

I want the same thing but with a normal variety.

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    $\begingroup$ This paper by D. Greb and S. Rollenske is relevant: arxiv.org/abs/1012.5940 . Namely it contains a criterion for when $\Omega_{V/k}$ is torsion free when $V$ is a cone over a smooth projective variety. Such cones are normal if the base projective variety is projectively normal. $\endgroup$ Commented Sep 16, 2020 at 8:54
  • $\begingroup$ Thank you. That was a very helpful recommendation. They give quite explicit examples of this phenomenon. $\endgroup$ Commented Sep 17, 2020 at 8:54

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