  This paper deals with the computation of sectional curvature for the
manifolds of $N$ landmarks (or feature points) in D dimensions, endowed with
the Riemannian metric induced by the group action of diffeomorphisms. The
inverse of the metric tensor for these manifolds (i.e. the cometric), when
written in coordinates, is such that each of its elements depends on at most 2D
of the ND coordinates. This makes the matrices of partial derivatives of the
cometric very sparse in nature, thus suggesting solving the highly non-trivial
problem of developing a formula that expresses sectional curvature in terms of
the cometric and its first and second partial derivatives (we call this Mario's
formula). We apply such formula to the manifolds of landmarks and in particular
we fully explore the case of geodesics on which only two points have non-zero
momenta and compute the sectional curvatures of 2-planes spanned by the
tangents to such geodesics. The latter example gives insight to the geometry of
the full manifolds of landmarks.
