Some elementary examples of non-liftable varieties

Achinger, Piotr; Zdanowicz, Maciej

doi:10.1090/proc/13622

Some elementary examples of non-liftable varieties
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by Piotr Achinger and Maciej Zdanowicz PDF

Proc. Amer. Math. Soc. 145 (2017), 4717-4729 Request permission

Abstract:

We present some simple examples of smooth projective varieties in positive characteristic, arising from linear algebra, which do not admit a lifting neither to characteristic zero, nor to the ring of Witt vectors of length $2$. Our first construction is the blow-up of the graph of the Frobenius morphism of a homogeneous space. The second example is a blow-up of $\mathbb {P}^3$ in a ‘purely characteristic-$p$’ configuration of points and lines.

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