  Projective invariance is a symmetry of the Palatini version of General
Relativity which is not present in the metric formulation. The fact that the
Riemann tensor changes nontrivially under projective transformations implies
that, unlike in the usual metric approach, in the Palatini formulation this
tensor is subject to a gauge freedom, which allows some ambiguities even in its
scalar contractions. In this sense, we show that for the Schwarzschild solution
there exists a projective gauge in which the (affine) Kretschmann scalar,
$K\equiv {R^\alpha}_{\beta\mu\nu}{R_\alpha}^{\beta\mu\nu}$, can be set to
vanish everywhere. This puts forward that the divergence of curvature scalars
may, in some cases, be avoided by a gauge transformation of the connection.
