Projective models of Enriques surfaces in scrolls

We study Cossec's ? ‐function, which is defined for divisors with positive self‐intersection on an Enriques surface. In this paper we study the existence of pairs (C ², ? (C )) with C an irreducible curve. The ? ‐function gives in a natural way scrolls containing Enriques surfaces. We compute scroll types to some of these scrolls. (© 2006 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)