Skip to main content
Log in

Interpolation Problems for Vector Bundles on Algebraic Curves

  • Published:
Acta Applicandae Mathematica Aims and scope Submit manuscript

Abstract

In this paper we study meromorphic maps between vector bundles on a Riemann surface. We are mainly interested in stable vector bundles. For a huge number of numerical data we prove the existence of a meromorphic map between two vector bundles with a prescribed number of zeroes and a prescribed number of poles.

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

Access this article

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

Instant access to the full article PDF.

Similar content being viewed by others

References

  1. Arbarello, E., Cornalba, M., Griffiths, P. and Harris, J.: Geometry of Algebraic Curves, Vol. I, Grundlehren der math. Wiss. 267, Springer-Verlag, New York, 1985.

    Google Scholar 

  2. Ball, J. A. and Vinnikov, V.: Zero-pole interpolation for meromorphic matrix function on an algebraic curve and transfer functions of 2D systems, Acta Appl. Math. 45(1996), 239-316.

    Google Scholar 

  3. Ball, J. A. and Vinnikov, V.: Zero-pole interpolation for matrix meromorphic functions on a compact Riemann surface and a matrix Fay trisecant identity, Preprint alg-geom / 9712028.

  4. Ballico, E.: On the osculating bundles of curves in P n, J. Algebra(to appear).

  5. Ballico, E.: Brill-Noether theory for vector bundles on projective curves, Math. Proc. Cambridge Philos. Soc.(to appear).

  6. Bradlow, S. B., Daskalopoulos, G. D., Garcia-Prada, O. and Wentworth, R. A.: Stable augmented bundles over Riemann surfaces, in: Symposium on Vector Bundles in Algebraic Geometry, Durham 1993, London Math. Soc. Lecture Notes Series, Cambridge University Press, Cambridge, 1995, pp. 15-67.

    Google Scholar 

  7. Brambila-Paz, L., Grzegorczyk, I. and Newstead, P. E.: Geography of Brill-Noether loci for small slopes, J. Algebraic Geom. 6(1997), 645-669.

    Google Scholar 

  8. Gunning, R. C.: Lectures on Vector Bundles over Riemann Surfaces, Princeton University Press, Princeton, NJ, 1967.

    Google Scholar 

  9. Hartshorne, R.: Algebraic Geometry, Springer-Verlag, Berlin, New York, 1977.

    Google Scholar 

  10. Hirschowitz, H.: Problèmes de Brill-Noether en rank supérieur, Unpublished preprint partially printed as ref. [11].

  11. Hirschowitz, H.: Problèmes de Brill-Noether en rank supérieur, C.R. Acad. Sci. Paris, Série I 307(1988), 153-156.

    Google Scholar 

  12. Kleiman, S.: Geometry of Grassmannians and applications to splitting bundles and smoothing cycles, Publ. I.H.E.S. 36(1969), 281-297.

    Google Scholar 

  13. Kleiman, S.: The transversality of a general translate, Compositio Math. 28(1974), 287-297.

    Google Scholar 

  14. Lange, H.: Zur Klassification von Regelmannigfaltigkeiten, Math. Ann. 262(1984), 447-459.

    Google Scholar 

  15. Lange, H. and Narasimhan, M. S.: Maximal subbundles of rank two vector bundles on curves, Math. Ann. 266(1983), 55-72.

    Google Scholar 

  16. Mukai, S. and Sakai, F.: Maximal subbundles of vector bundles on a curve, Manuscripta Math. 52(1985), 251-256.

    Google Scholar 

  17. Narasimhan, M. S. and Ramanan, S.: Deformation of the moduli space of vector bundles over an algebraic curve, Ann. Math. 101(1975), 391-417.

    Google Scholar 

  18. Newstead, P. E.: Introduction to Moduli Problems and Orbit Spaces, Tata Inst. Lect. Notes, 1978.

  19. Seshadri, C.: Fibrés vectoriels sur les courbes algébriques, Astérisque 96, Soc. Math. France, 1982.

  20. Vinnikov, V.: in preparation.

Download references

Author information

Authors and Affiliations

Authors

Rights and permissions

Reprints and permissions

About this article

Cite this article

Ballico, E. Interpolation Problems for Vector Bundles on Algebraic Curves. Acta Applicandae Mathematicae 53, 229–245 (1998). https://doi.org/10.1023/A:1006016106965

Download citation

  • Issue Date:

  • DOI: https://doi.org/10.1023/A:1006016106965

Navigation