Hostname: page-component-586b7cd67f-r5fsc Total loading time: 0 Render date: 2024-11-22T20:48:38.247Z Has data issue: false hasContentIssue false
  • English
  • Français

ON AN EXAMPLE OF MUKAI

Published online by Cambridge University Press:  12 December 2011

H. LANGE ,
V. MERCAT  and
P. E. NEWSTEAD
H. LANGE
Affiliation:
Department Mathematik, Universität Erlangen-Nürnberg, Bismarckstraße 1½, D-91054 Erlangen, Germany e-mail: [email protected]
V. MERCAT
Affiliation:
5 rue Delouvain, 75019 Paris, France e-mail: [email protected]
P. E. NEWSTEAD
Affiliation:
Department of Mathematical Sciences, University of Liverpool, Peach Street, Liverpool L69 7ZL, UK e-mail: [email protected]
Rights & Permissions [Opens in a new window]

Abstract

Core share and HTML view are not available for this content. However, as you have access to this content, a full PDF is available via the ‘Save PDF’ action button.

In this paper we use an example of Mukai to construct semistable bundles of rank 3 with six independent sections on a general curve of genus 9 or 11 with Clifford index strictly less than the Clifford index of the curve. The example also allows us to show the non-emptiness of some Brill–Noether loci with negative expected dimension.

Keywords

Primary 14H60
Type
Research Article
Information
Glasgow Mathematical Journal , Volume 54 , Issue 2 , May 2012 , pp. 261 - 271
Copyright
Copyright © Glasgow Mathematical Journal Trust 2011

References

REFERENCES

1.Bradlow, S. B., García-Prada, O., Muñoz, V. and Newstead, P. E., Coherent systems and Brill–Noether theory, Int. J. Math. 14 (2003), 683–733.CrossRefGoogle Scholar
2.Farkas, G. and Ortega, A., The maximal rank conjecture and rank two Brill–Noether theory, Pure Appl. Math. Q. 7 (4) (2011), 1265–1296.CrossRefGoogle Scholar
3.Farkas, G. and Ortega, A., Higher rank Brill–Noether theory on sections of K3 surfaces, arXiv:1102.0276.Google Scholar
4.Grzegorczyk, I., Mercat, V. and Newstead, P. E., Stable bundles of rank 2 with 4 sections, Int. J. Math. to appear. arXiv:1006.1258v2.Google Scholar
5.Grzegorcyk, I. and Teixidor i Bigas, M., Brill–Noether theory for stable vector bundles, in Moduli spaces and vector bundles, London Mathematical Society Lecture Notes Series, vol. 359 (Cambridge University Press, Cambridge, UK, 2009), 29–50.CrossRefGoogle Scholar
6.Lange, H. and Newstead, P. E., Clifford indices for vector bundles on curves, in Affine flag manifolds and principal bundles (Trends in Mathematics, Birkhäuser, Basel, 2010), 165–202.CrossRefGoogle Scholar
7.Lange, H. and Newstead, P. E., Generation of vector bundles computing Clifford indices, Arch. Math. 94 (2010), 529–537.CrossRefGoogle Scholar
8.Lange, H. and Newstead, P. E., Lower bounds for Clifford indices in rank three, Math. Proc. Camb. Philos. Soc. 150 (2011), 23–33, doi:10.1017/S0305004110000502.CrossRefGoogle Scholar
9.Lange, H. and Newstead, P. E., Further examples of stable bundles of rank 2 with 4 sections, Pure Appl. Math. Q. 7 (4) (2011), 1517–1528.CrossRefGoogle Scholar
10.Lange, H. and Newstead, P. E., Vector bundles of rank 2 computing Clifford indices. to appear. arXiv:1012.0469.Google Scholar
11.Lazarsfeld, R., Brill–Noether–Petri without degeneration, J. Differ. Geom. 23 (1986), 299–307.CrossRefGoogle Scholar
12.Mercat, V., Clifford's theorem and higher rank vector bundles, Int. J. Math. 13 (2002), 785–796.CrossRefGoogle Scholar
13.Mukai, S., Curves and symmetric spaces, Proc. Jap. Acad. 68(ser. A) (1992), 7–10.Google Scholar
14.Mukai, S., Curves and symmetric spaces, Ann. Math. 173 (3) (2011), 1539–1558.Google Scholar
15.Mukai, S., Addendum to “Curves and symmetric spaces, II.” Addendum RIMS-1395 (2010).Google Scholar
16.Mumford, D., Theta characteristics of an algebraic curve, Ann. Scient. Éc. Norm. Sup., 4e série, t. 4 (1971), 181–192.Google Scholar
17.Paranjape, K. and Ramanan, S., On the canonical ring of a curve, in Algebraic geometry and commutative algebra, vol. II (Hijikara, H. et al. , Editors) (Kinokuniya, Tokyo, 1988), 503–516.CrossRefGoogle Scholar