  Given a divisorial discrete valuation 'centered at infinity' on C[x,y], we
show that its sign on C[x,y] (i.e. whether it is negative or non-positive on
non-constant polynomials) is completely determined by the sign of its value on
the 'last key form' (key forms being the avatar of 'key polynomials' of
valuations (introduced by [Maclane, 1936]) in 'global coordinates'). The proof
involves computations related to the cone of curves on certain
compactifications of C^2 and gives a characterization of the divisorial
valuations centered at infinity whose 'skewness' can be interpreted in terms of
the 'slope' of an extremal ray of these cones, yielding a generalization of a
result of [Favre-Jonsson, 2007]. A by-product of these arguments is a
characterization of valuations which 'determine' normal compactifications of
C^2 with one irreducible curve at infinity in terms of an associated 'semigroup
of values'.
