  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.
