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Some elementary examples of non-liftable schemes (1606.04027v1)

Published 13 Jun 2016 in math.AG

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 second Witt vectors. 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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