  Two very different formulations of the tree-level S-matrix of N=8 Einstein
supergravity in terms of rational maps are known to exist. In both
formulations, the computation of a scattering amplitude of n particles in the k
R-charge sector involves an integral over the moduli space of certain
holomorphic maps of degree d=k-1. In this paper we show that both formulations
can be simplified when written in a manifestly parity invariant form as
integrals over holomorphic maps of bi-degree (d,n-d-2). In one formulation the
full integrand becomes directly the product of the resultants of each of the
two maps defining the one of bi-degree (d,n-d-2). In the second formulation, a
very different structure appears. The integrand contains the determinant of a
(n-3)x(n-3) matrix and a 'Jacobian'. We prove that the determinant is a
polynomial in the coefficients of the maps and contains the two resultants as
factors.
