On the geometric genus of reducible surfaces and degenerations of surfaces to unions of planes

In this paper we study some properties of degenerations of surfaces whose general fibre is a smooth projective algebraic surface and whose central fibre is a reduced, connected surface X in P^r, r > 2, which is assumed to be a union of planes. Here we present a first set of results on the subject; other aspects are still work in progress and will appear later on. Our original motivation has been a series of papers by Guido Zappa which appeared in the 1940--50's regarding degenerations of scrolls to unions of planes and the computation of bounds for the topological invariants of an arbitrary smooth projective surface which is assumed to degenerate to a union of planes.