Projective Normality of Special Scrolls

Abstract

We study the projective normality of a linearly normal special scroll R of degree d and speciality i over a smooth curve X of genus g. We relate it with the Clifford index of the base curve X. If d ≥ 4g − 2i − Cliff(X) + 1, i ≥ 3 and R is smooth, we prove that the projective normality of the scroll is equivalent to the projective normality of its directrix curve of minimum degree.