101
Views
9
CrossRef citations to date
0
Altmetric
Original Articles

Moduli Spaces of Coherent Systems of Small Slope on Algebraic Curves

, , , &
Pages 2649-2678 | Received 10 Dec 2007, Published online: 22 Jul 2009

REFERENCES

  • Atiyah , M. F. ( 1957 ). Vector bundles over an elliptic curve . Proc. London Math. Soc. 7 ( 3 ): 414 – 452 .
  • Bhosle , U. N. , Brambila-Paz , L. , Newstead , P. E. ( 2008 ). On coherent systems of type (n, d, n + 1) on Petri curves . Manuscripta Math. 126 : 409 – 441 .
  • Bradlow , S. B. , García-Prada , O. ( 2002 ). An application of coherent systems to a Brill–Noether problem . J. Reine Angew. Math. 551 : 123 – 143 .
  • Bradlow , S. B. , García-Prada , O. , Mercat , V. , Mu\ noz , V. , Newstead , P. E. ( 2007 ). On the geometry of moduli spaces of coherent systems on algebraic curves . Internat. J. Math. 18 : 411 – 453 .
  • Bradlow , S. B. , García-Prada , O. , Muñoz , V. , Newstead , P. E. ( 2003 ). Coherent Systems and Brill–Noether theory . Internat. J. Math. 14 : 683 – 733 .
  • Brambila-Paz , L. ( 2008 ). Non-emptiness of moduli spaces of coherent systems . Internat. J. Math. 19 : 777 – 799 .
  • Brambila-Paz , L. , Grzegorczyk , I. , Newstead , P. E. ( 1997 ). Geography of Brill–Noether loci for small slopes . J. Algebraic Geometry 6 : 645 – 669 .
  • He , M. ( 1998 ). Espaces de modules de systèmes cohérents . Internat. J. Math. 9 : 545 – 598 .
  • King , A. D. , Newstead , P. E. ( 1995 ). Moduli of Brill–Noether pairs on algebraic curves . Internat. J. Math. 6 : 733 – 748 .
  • Lange , H. , Newstead , P. E. ( 2004 ). Coherent systems of genus 0 . Internat. J. Math. 15 : 409 – 424 .
  • Lange , H. , Newstead , P. E. ( 2005 ). Coherent systems on elliptic curves . Internat. J. Math. 16 : 787 – 805 .
  • Lange , H. , Newstead , P. E. ( 2007 ). Coherent systems of genus 0 II: existence results for k ≥ 3 . Internat. J. Math. 18 : 363 – 393 .
  • Le Potier , J. ( 1995 ). Faisceaux semi-stables et systèmes cohérents . In: Hitchin , N. J. , Newstead , P. E. , Oxbury , W. M. , eds. Vector Bundles in Algebraic Geometry, Durham 1993 . LMS Lecture Notes Series . Vol. 208 . Cambridge : Cambridge University Press , pp. 179 – 239 .
  • Mercat , V. ( 1999 ). Le problème de Brill–Noether pour des fibrés stables de petite pente . J. Reine Angew. Math. 506 : 1 – 41 .
  • Mercat , V. ( 2001 ). Fibrés stables de pente 2 . Bull. London Math. Soc. 33 : 535 – 542 .
  • Narasimhan , M. S. , Ramanan , S. ( 1965 ). Deformation of the moduli space of vector bundles over an algebraic curve . Ann. Math. 82 ( 2 ): 540 – 567 .
  • Paranjape , K. , Ramanan , S. ( 1988 ). On the canonical ring of a curve . Algebraic Geometry and Commutative Algebra , Vol. II. Kinokuniya, Tokyo , pp. 503 – 516 .
  • Raghavendra , N. , Vishwanath , P. A. ( 1994 ). Moduli of pairs and generalized theta divisors . Tôhoku Math. J. 46 : 321 – 340 .
  • Teixidor i. Bigas , M. ( 2008 ). Existence of coherent systems II . Internat. J. Math. 19 : 1269 – 1283 .
  • Communicated by L. Ein.

Reprints and Corporate Permissions

Please note: Selecting permissions does not provide access to the full text of the article, please see our help page How do I view content?

To request a reprint or corporate permissions for this article, please click on the relevant link below:

Academic Permissions

Please note: Selecting permissions does not provide access to the full text of the article, please see our help page How do I view content?

Obtain permissions instantly via Rightslink by clicking on the button below:

If you are unable to obtain permissions via Rightslink, please complete and submit this Permissions form. For more information, please visit our Permissions help page.