Predegree polynomials of plane configurations in P³

PGL(4) acts naturally on the projective space P^N parameterizing surfaces in P³ (characteristic 0). The orbit of a surface under this action is the image of a map PGL(4) < P¹⁵ ---> P^N. The orbit is a natural and interesting object to study. Its predegree is defined as the degree of the orbit closure multiplied by the degree of the above map restricted over a P^j, j being the dimension of the orbit. We find the predegrees and other invariants of all surfaces supported on unions of (possibly nonreduced) planes. The information is encoded in the so called predegree polynomials which posses nice multiplicative properties allowing us to easily compute the predegree (polynomials) of various special configurations.