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.

Key Words:

• Projective normality
• Ruled Surfaces

2000 Mathematics Subject Classification:

• Primary 14J26
• Secondary 14H51, 14H60

ACKNOWLEDGMENTS

The first author was supported by an F.P.U. fellowship of Spanish Government and the second author was partially supported by Xunta de Galicia, project PGIDITOPXIA20702PR.

Notes

Communicated by L. Ein.