Scrollar syzygies of general canonical curves with genus ≤8

Bothmer, Hans-Christian

doi:10.1090/S0002-9947-06-04353-4

Scrollar syzygies of general canonical curves with genus $\le 8$

Author: Hans-Christian Graf v. Bothmer
Journal: Trans. Amer. Math. Soc. 359 (2007), 465-488
MSC (2000): Primary 13D02, 14H45, 14C20
DOI: https://doi.org/10.1090/S0002-9947-06-04353-4
Published electronically: September 12, 2006
MathSciNet review: 2255182
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Abstract: We prove that for a general canonical curve $C \subset \mathbb {Z}^{g-1}$ of genus $g$, the space of ${\lceil \frac {g-5}{2}\rceil }$th (last) scrollar syzygies is isomorphic to the Brill-Noether locus $C^1_{\lceil \frac {g+2}{2} \rceil }$. Schreyer has conjectured that these scrollar syzygies span the space of all ${\lceil \frac {g-5}{2} \rceil }$th (last) syzygies of $C$. Using Mukai varieties we prove this conjecture for genus $6$, $7$ and $8$.

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