Classification of reducible plane curves (Q1117997)

Here it is studied the birational geometry (which is part of ``Iitaka's program'') of a pair (S,C) with S smooth complete rational surface and \(C\subset S\) is a curve with 2 irreducible components. In particular it is proved that if \(S={\mathbb{P}}^ 2 \) C is transformed by a Cremona transformation into the union of two lines if and only if \(h^ 0(S,[2K_ S+2C])=0\).