Syzygies of canonical curves and special linear series

0. Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . 105 1. Line Bundles on Scrolls . . . . . . . . . . . . . . . . . . . . . . . 109 2. Scrolls and Pencils . . . . . . . . . . . . . . . . . . . . . . . . . 113 3. Syzygies of a Subvariety of a Scroll . . . . . . . . . . . . . . . . . . 115 4. Canonical Curves . . . . . . . . . . . . . . . . . . . . . . . . . 118 5. On the Equation of Rational Surfaces . . . . . . . . . . . . . . . . . . 121 6. d-Gonal Curves for d<5 . . . . . . . . . . . . . . . . . . . . . . 126 7. Proof of the Main Result . . . . . . . . . . . . . . . . . . . . . . 131 References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 136

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