A note on a Brill-Noether locus over a non-hyperelliptic curve of genus 4

Sukmoon Huh

Open Mathematics (2009)

  • Volume: 7, Issue: 4, page 617-622
  • ISSN: 2391-5455

Abstract

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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.

How to cite

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Sukmoon Huh. "A note on a Brill-Noether locus over a non-hyperelliptic curve of genus 4." Open Mathematics 7.4 (2009): 617-622. <http://eudml.org/doc/269302>.

@article{SukmoonHuh2009,
abstract = {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.},
author = {Sukmoon Huh},
journal = {Open Mathematics},
keywords = {Moduli; Hirzebruch surface; Stable sheaf; Brill-Noether loci; moduli space; stable bundle; Brill-Noether locus},
language = {eng},
number = {4},
pages = {617-622},
title = {A note on a Brill-Noether locus over a non-hyperelliptic curve of genus 4},
url = {http://eudml.org/doc/269302},
volume = {7},
year = {2009},
}

TY - JOUR
AU - Sukmoon Huh
TI - A note on a Brill-Noether locus over a non-hyperelliptic curve of genus 4
JO - Open Mathematics
PY - 2009
VL - 7
IS - 4
SP - 617
EP - 622
AB - 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.
LA - eng
KW - Moduli; Hirzebruch surface; Stable sheaf; Brill-Noether loci; moduli space; stable bundle; Brill-Noether locus
UR - http://eudml.org/doc/269302
ER -

References

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  1. [1] Beauville A., Complex algebraic surfaces, second ed., London Mathematical Society Student Texts, 34, Cambridge University Press, Cambridge, 1996 Zbl0849.14014
  2. [2] Hartshorne R., Algebraic geometry, Graduate Texts in Mathematics, 52, Springer-Verlag, New York, 1977 Zbl0367.14001
  3. [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. [4] Huybrechts D., Lehn M., The geometry of moduli spaces of sheaves, Aspects of Mathematics, E31, Friedr. Vieweg & Sohn, Braunschweig, 1997 Zbl0872.14002
  5. [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] Zbl0578.14044
  6. [6] Okonek C, Schneider M., Spindler H., Vector bundles on complex projective spaces, Progress in Mathematics, vol. 3, Birkhäuser Boston, Boston, MA, 1980 Zbl0438.32016
  7. [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] Zbl0898.14014

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