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Transactions of the American Mathematical Society
Transactions of the American Mathematical Society
ISSN 1088-6850(online) ISSN 0002-9947(print)

 

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
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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Additional Information

Hans-Christian Graf v. Bothmer
Affiliation: Laboratoire J.-A. Dieudonné, Université de Nice, Parc Valrose, 06108 Nice cedex 2, France
Address at time of publication: Institiut für Algebraische Geometrie, Universität Hannover, Welfengarten 1, D-30167 Hannover, Germany
Email: bothmer@math.uni-hannover.de

DOI: http://dx.doi.org/10.1090/S0002-9947-06-04353-4
PII: S 0002-9947(06)04353-4
Received by editor(s): November 12, 2002
Published electronically: September 12, 2006
Additional Notes: This work was supported by the Schwerpunktprogramm “Global Methods in Complex Geometry” of the Deutsche Forschungs Gemeinschaft and Marie Curie Fellowship HPMT-CT-2001-001238
Article copyright: © Copyright 2006 American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication.