On rational and ruled double planes

Following the ideas of Castelnuovo and Enriques, we classify the birational equivalence classes of double planes which are rational or ruled surfaces. In order to do this, we prove that the vanishing of the m-adjoint linear system to the branch curve of the canonical resolution of a double plane, for m≥2, is a necessary and sufficient condition for the ruledness of the double plane. Received: May 18, 2000?Published online: October 30, 2002 Partially supported by E.C. project EAGER, contract n. HPRN-CT-2000-00099