  We construct an invariant of parametrized generic real algebraic surfaces in
RP^3 which generalizes the Brown invariant of immersed surfaces from smooth
topology. The invariant is constructed using the self intersection, which is a
real algebraic curve with points of three local characters: the intersection of
two real sheets, the intersection of two complex conjugate sheets or a Whitney
umbrella. The Brown invariant was expressed through a self linking number of
the self intersection by Kirby and Melvin. We extend the definition of this
self linking number to the case of parametrized generic real algebraic
surfaces.
