Skip to main content
Log in

On Linear Systems of Curves on Rational Scrolls

  • Published:
Geometriae Dedicata Aims and scope Submit manuscript

Abstract

In this paper we prove a conjecture on the dimension of linear systems, with base points of multiplicity 2 and 3, on an Hirzebruck surface.

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. Ciliberto, C. and Miranda, R.: Linear systems of plane curves with base points of equal multiplicity,Trans. Amer. Math. Soc.

  2. Ciliberto, C. and Miranda, R.: Degenerations of planar linear systems, J. Reine Angew. Math. 501 (1998), 191–220.

    Google Scholar 

  3. Geramita, A. V., Gimigliano, A. and Harbourne, B.: Projectively normal but superabundant embeddings of rational surfaces in projective space, J. Algebra 169(3) (1994), 791–804.

    Google Scholar 

  4. Greuel, G.-M., Lossen, C. and Shustin, E.: Plane curves ofminimal degree with prescribed singularities, Invent. Math. 133(3) (1998), 539–580.

    Google Scholar 

  5. Harbourne, B.: Points in good position in ℙ2, In: Zero-Dimensional Schemes (Ravello, 1992). de Gruyter, Berlin, 1994, pp. 213–229.

    Google Scholar 

  6. Harbourne, B.: Birational morphisms of rational surfaces, J. Algebra 190(1) (1997), 145–162.

    Google Scholar 

  7. Harbourne, B.: Free resolutions of fat point ideals on ℙ2. J. Pure Appl. Algebra 125(1–3) (1998), 213–234.

    Google Scholar 

  8. Hartshorne, R.: Algebraic Geometry, Graduate Texts in Math. 52, Spinger-Verlag, New York.

  9. Hirschowitz, A.: Une conjecture pour la cohomologie des diviseurs sur les surfaces rationnelles génériques, J. Reine Angew. Math. 397 (1989), 208–213.

    Google Scholar 

  10. Ran, Z.: Enumerative geometry of singular plane curves, Invent. Math. 97(3) (1989), 447–465.

    Google Scholar 

  11. Shustin, E.: Real plane algebraic curves with prescribed singularities, Topology 32(4) (1993), 845–856.

    Google Scholar 

  12. Walker, R. J.: Algebraic Curves, Dover, New York, 1962.

    Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Rights and permissions

Reprints and permissions

About this article

Cite this article

Laface, A. On Linear Systems of Curves on Rational Scrolls. Geometriae Dedicata 90, 127–144 (2002). https://doi.org/10.1023/A:1014958409472

Download citation

  • Issue Date:

  • DOI: https://doi.org/10.1023/A:1014958409472

Navigation