Skip to main content
SpringerLink
Log in

On the gonality of nodal curves

  • Published:
Geometriae Dedicata Aims and scope Submit manuscript

Abstract

Here we prove that for every n≥33 and every t≤(n 2+3n)/6, the normalization Y of a general plane curve C of degree n and with t nodes has no g 1 b with b<n−2 and only g 1 n−2 and g 1 n−1 induced by a pencil of lines through a point of C. Recently, Coppens and Kato proved stronger results.

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. d'Almeida, J., ‘Courbes de l'espace projectif; Séries linéaires incomplète et multisecantes’, J. Reine angew. Math. 370 (1986), 30–51.

    Google Scholar 

  2. Arbarello, E. and Cornalba, M., ‘Footnotes to a paper of Beniamino Segre’, Math. Ann. 256 (1981), 341–362.

    Google Scholar 

  3. Arbarello, E., Cornalba, M., Griffiths, P. and Harris, J., Geometry of Algebraic Curves, Vol. I, Springer-Verlag, 1984.

  4. Brun, J., ‘Les fibres de range deux sur P 2 et leurs sections’, Bull. Soc. Math. France 107 (1979), 457–473.

    Google Scholar 

  5. Brun, J. and Hirschowitz, A., ‘Le problème de Brill-Noether pour les ideaux de P 2’, Ann. Sci. École. Norm. Sup. 20 (1987), 171–200.

    Google Scholar 

  6. Coppens, M. and Kato, T., ‘The gonality of smooth curves with plane models’ (preprint, 1990).

  7. Diaz, S. and Harris, J., ‘Geometry of the Severi variety’, Trans. Amer. Math. Soc. 309 (1988), 1–34.

    Google Scholar 

  8. Griffiths, P. and Harris, J., Principles of Algebraic Geometry, Wiley, New York, 1978.

    Google Scholar 

  9. Harris, J., ‘On the Severi problem’, Invent. Math. 84 (1986), 445–461.

    Google Scholar 

  10. Hartshorne, R., ‘Stable reflexive sheaves’, Math. Ann. 254 (1980), 121–176.

    Google Scholar 

  11. Nobile, A., ‘Families of curves on surfaces’, Math. Z. 187 (1984), 453–470.

    Google Scholar 

  12. Ran, Z., ‘On nodal curves’, Invent. Math. 86 (1986), 529–534.

    Google Scholar 

  13. Ran, Z., ‘Enumerative geometry of singular plane curves’, Invent. Math. 97 (1989), 447–465.

    Google Scholar 

  14. Reider, I., ‘Vector bundles of rank 2 and linear systems on algebraic surfaces’, Ann. of Math. 127 (1988), 309–316.

    Google Scholar 

  15. Tannenbaum, A., ‘Families of curves with nodes’, Compositio Math. 41 (1980), 107–126.

    Google Scholar 

  16. Tannenbaum, A., ‘Families of curves with nodes on K-3 surfaces’, Math. Ann. 260 (1982), 239–253.

    Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Dipartimento di Matematica, Università di Trento, I-38050, Povo (Trento), Italy

    Edoardo Ballico

Authors
  1. Edoardo Ballico
    View author publications

    You can also search for this author in PubMed Google Scholar

Rights and permissions

Reprints and permissions

About this article

Cite this article

Ballico, E. On the gonality of nodal curves. Geom Dedicata 37, 357–360 (1991). https://doi.org/10.1007/BF00181412

Download citation

  • Received:

  • Revised:

  • Issue Date:

  • DOI: https://doi.org/10.1007/BF00181412

Keywords

Search

Navigation