Skip to main content
SpringerLink
Log in

Holomorphic triples of genus 0

  • Research Article
  • Published:
Central European Journal of Mathematics

Abstract

Here we study the relationship between the stability of coherent systems and the stability of holomorphic triples over a curve of arbitrary genus. Moreover we apply these results to study some properties and give some examples of holomorphic triples on the projective line.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Similar content being viewed by others

References

  1. Bradlow S.B., Daskalopoulos G.D., García-Prada O., Wentworth R., Stable augmented bundles over Riemann surfaces, Vector bundles in algebraic geometry (Durham 1993), London Math. Soc. Lecture Notes Ser., 1995, 208, 15–67

  2. Bradlow S.B., García-Prada O., An application of coherent systems to a Brill-Noether problem, J. Reine Angew. Math., 2002, 551, 123–143

    MATH  MathSciNet  Google Scholar 

  3. Bradlow S.B., García-Prada O., Stable triples equivariant bundles and dimensional reduction, Math. Ann., 1996, 304, 225–252

    Article  MATH  MathSciNet  Google Scholar 

  4. Bradlow S.B., García-Prada O., Gothen P.B., Moduli spaces of holomorphic triples over compact Riemann surfaces, Math. Ann., 2004, 328, 299–351

    Article  MATH  MathSciNet  Google Scholar 

  5. Bradlow S.B., García-Prada O., Gothen P.B., Homotopy groups of moduli spaces of representations, preprint available at http://arxiv.org/abs/math/0506444 v2

  6. Bradlow S.B., García-Prada O., Mercat V., Muñoz V., Newstead P.E., On the geometry of moduli spaces of coherent systems on algebraic curves, preprint available at http://arxiv.org/abs/math/0407523 v5

  7. Bradlow S.B., García-Prada O., Munoz V., Newstead P.E., Coherent systems and Brill-Noether theory, Internat. J. Math., 2003, 14, 683–733

    Article  MATH  MathSciNet  Google Scholar 

  8. Grothendieck A., Sur la classification des fibrés holomorphes sur la sphère de Riemann, Amer. J. Math., 1957, 79, 121–138 (in French)

    Article  MATH  MathSciNet  Google Scholar 

  9. Lange H., Newstead P.E., Coherent systems on elliptic curves, Internat. J. Math., 2005, 16, 787–805

    Article  MATH  MathSciNet  Google Scholar 

  10. Lange H., Newstead P.E., Coherent systems of genus 0, Internat. J. Math., 2004, 15, 409–424

    Article  MATH  MathSciNet  Google Scholar 

  11. Lange H., Newstead P.E., Coherent systems of genus 0 II Existence results for k ≥ 3, Internat. J. Math., 2007, 18, 363–393

    Article  MATH  MathSciNet  Google Scholar 

  12. Pasotti S., Prantil F., Holomorphic triples on elliptic curves, Results Math., 2007, 50, 227–239

    Article  MathSciNet  Google Scholar 

  13. Schmitt A., A universal construction for the moduli spaces of decorated vector bundles, Habilitationsschrift, University of Essen, 2000

Download references

Author information

Authors and Affiliations

  1. Dipartimento di Matematica e Fisica, Universita Cattolica, via Musei 41, 25121, Brescia, Italy

    Stefano Pasotti

  2. Department of Mathematics, University of Trento, via Sommarive 14, 38050, Povo (TN), Italy

    Francesco Prantil

Authors
  1. Stefano Pasotti
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Francesco Prantil
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Stefano Pasotti.

About this article

Cite this article

Pasotti, S., Prantil, F. Holomorphic triples of genus 0. centr.eur.j.math. 6, 129–142 (2008). https://doi.org/10.2478/s11533-008-0008-x

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.2478/s11533-008-0008-x

MSC

Keywords

Search

Navigation