... Flamini, and R. Miranda*AbstractIn this paper we study some properties of reducible surfaces, in particularof unions of planes. When the surface is the central fibre of an embedded flatdegeneration ... projective geometry, we refer the reader to e.g. [11], [17] and [25]).Theorem 5.20 (del Pezzo, [10]). Let X be an irreducible, nondegener-ate, linearly normal surface of degree r in P r . Then one ... the Riemann-Rochtheorem.Lemma 5.21. Let D ⊂ P r be a reduced (possibly reducible), nondegenerate and linearly normal curve of degree r + d in P r , with 0 d< ;r. Thenpa(D)=d.Theorem...