Dimitre Tzigantchev— FSU

**PGL**(4) acts naturally on the projective space
**P**^{N} parameterizing surfaces in
**P**^{3} (characteristic 0). The orbit of a
surface under this action is the image of a map
**PGL**(4) < **P**^{15} --->
**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.