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 | References | Similar Articles | Additional Information
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
MR Author ID:
724323
Email:
bothmer@math.uni-hannover.de
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.