Some elementary examples of non-liftable schemes
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 P3 in a 'purely characteristic-p' configuration of points and lines.
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