Syzygies of 5-Gonal Canonical Curves

We show that for 5-gonal curves of odd genus $g≥ 13$ and even genus $g≥ 28$ the $\lceil \frac{g-1}2\rceil$-th syzygy module of the curve is not determined by the syzygies of the scroll swept out by the special pencil of degree 5.

2010 Mathematics Subject Classification: 13D02,14H51

Keywords and Phrases: syzygies, canonical curves, gonality, special divisor

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