Geodesic
ON AN EXAMPLE OF MUKAI
Glasgow mathematical journal, Tome 54 (2012) no. 2, pp. 261-271

Voir la notice de l'article provenant de la source Cambridge University Press

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.
DOI : 10.1017/S0017089511000577
Mots-clés : Primary 14H60 
LANGE, H.; MERCAT, V.; NEWSTEAD, P. E. ON AN EXAMPLE OF MUKAI. Glasgow mathematical journal, Tome 54 (2012) no. 2, pp. 261-271. doi: 10.1017/S0017089511000577
@article{10_1017_S0017089511000577,
     author = {LANGE, H. and MERCAT, V. and NEWSTEAD, P. E.},
     title = {ON {AN} {EXAMPLE} {OF} {MUKAI}},
     journal = {Glasgow mathematical journal},
     pages = {261--271},
     year = {2012},
     volume = {54},
     number = {2},
     doi = {10.1017/S0017089511000577},
     url = {http://geodesic.mathdoc.fr/articles/10.1017/S0017089511000577/}
}
TY  - JOUR
AU  - LANGE, H.
AU  - MERCAT, V.
AU  - NEWSTEAD, P. E.
TI  - ON AN EXAMPLE OF MUKAI
JO  - Glasgow mathematical journal
PY  - 2012
SP  - 261
EP  - 271
VL  - 54
IS  - 2
UR  - http://geodesic.mathdoc.fr/articles/10.1017/S0017089511000577/
DO  - 10.1017/S0017089511000577
ID  - 10_1017_S0017089511000577
ER  - 
%0 Journal Article
%A LANGE, H.
%A MERCAT, V.
%A NEWSTEAD, P. E.
%T ON AN EXAMPLE OF MUKAI
%J Glasgow mathematical journal
%D 2012
%P 261-271
%V 54
%N 2
%U http://geodesic.mathdoc.fr/articles/10.1017/S0017089511000577/
%R 10.1017/S0017089511000577
%F 10_1017_S0017089511000577

[1] 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. Google Scholar | DOI

[2] 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. Google Scholar | DOI

[3] 3.Farkas, G. and Ortega, A., Higher rank Brill–Noether theory on sections of K3 surfaces, arXiv:1102.0276. Google Scholar

[4] 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] 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. Google Scholar | DOI

[6] 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. Google Scholar | DOI

[7] 7.Lange, H. and Newstead, P. E., Generation of vector bundles computing Clifford indices, Arch. Math. 94 (2010), 529–537. Google Scholar | DOI

[8] 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. Google Scholar | DOI

[9] 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. Google Scholar | DOI

[10] 10.Lange, H. and Newstead, P. E., Vector bundles of rank 2 computing Clifford indices. to appear. arXiv:1012.0469. Google Scholar

[11] 11.Lazarsfeld, R., Brill–Noether–Petri without degeneration, J. Differ. Geom. 23 (1986), 299–307. Google Scholar | DOI

[12] 12.Mercat, V., Clifford's theorem and higher rank vector bundles, Int. J. Math. 13 (2002), 785–796. Google Scholar | DOI

[13] 13.Mukai, S., Curves and symmetric spaces, Proc. Jap. Acad. 68(ser. A) (1992), 7–10. Google Scholar

[14] 14.Mukai, S., Curves and symmetric spaces, Ann. Math. 173 (3) (2011), 1539–1558. Google Scholar

[15] 15.Mukai, S., Addendum to “Curves and symmetric spaces, II.” Addendum RIMS-1395 (2010). Google Scholar

[16] 16.Mumford, D., Theta characteristics of an algebraic curve, Ann. Scient. Éc. Norm. Sup., 4e série, t. 4 (1971), 181–192. Google Scholar

[17] 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. Google Scholar | DOI

Cité par Sources :