We prove that a certain Brill-Noether locus over a non-hyperelliptic curve C of genus 4, is isomorphic to the Donagi-Izadi cubic threefold in the case when the pencils of the two trigonal line bundles of C coincide.
@article{bwmeta1.element.doi-10_2478_s11533-009-0045-0,
author = {Sukmoon Huh},
title = {A note on a Brill-Noether locus over a non-hyperelliptic curve of genus 4},
journal = {Open Mathematics},
volume = {7},
year = {2009},
pages = {617-622},
zbl = {1194.14051},
language = {en},
url = {http://dml.mathdoc.fr/item/bwmeta1.element.doi-10_2478_s11533-009-0045-0}
}
Sukmoon Huh. A note on a Brill-Noether locus over a non-hyperelliptic curve of genus 4. Open Mathematics, Tome 7 (2009) pp. 617-622. http://gdmltest.u-ga.fr/item/bwmeta1.element.doi-10_2478_s11533-009-0045-0/
[1] Beauville A., Complex algebraic surfaces, second ed., London Mathematical Society Student Texts, 34, Cambridge University Press, Cambridge, 1996 | Zbl 0849.14014
[2] Hartshorne R., Algebraic geometry, Graduate Texts in Mathematics, 52, Springer-Verlag, New York, 1977 | Zbl 0367.14001
[3] Huh S., A moduli space of stable sheaves on a smooth quadric in ℙ3, preprint available at http://arxiv.org/abs/0810.4392
[4] Huybrechts D., Lehn M., The geometry of moduli spaces of sheaves, Aspects of Mathematics, E31, Friedr. Vieweg & Sohn, Braunschweig, 1997 | Zbl 0872.14002
[5] Lange H., Higher secant varieties of curves and the theorem of Nagata on ruled surfaces, Manuscripta Math., 1984, 47, 263–269 http://dx.doi.org/10.1007/BF01174597[Crossref] | Zbl 0578.14044
[6] Okonek C, Schneider M., Spindler H., Vector bundles on complex projective spaces, Progress in Mathematics, vol. 3, Birkhäuser Boston, Boston, MA, 1980 | Zbl 0438.32016
[7] Oxbury W.M., Pauly C, Previato E., Subvarieties of SUC(2) and 2ν-divisors in the Jacobian, Trans. Amer. Math. Soc., 1998, 350(9), 3587–3614 http://dx.doi.org/10.1090/S0002-9947-98-02148-5[Crossref] | Zbl 0898.14014