Introduction to Special Divisors

  • E. Arbarello
  • M. Cornalba
  • P. A. Griffiths
  • J. Harris
Part of the Grundlehren der mathematischen Wissenschaften book series (GL, volume 267)

Abstract

In this chapter we shall begin our study of linear series on smooth curves. Our central question is: What are the limitations on the dimension r(D) of a complete linear series | D | ? The first result in this direction is the classical Clifford theorem. After discussing this, in a somewhat different vein, we shall prove Castelnuovo’s bound on the genus of a curve in projective r-space. This will lead to Max Noether’s theorem on the projective normality of canonical curves, to a detailed study of extremal curves in r-space and to a brief presentation of Petri’s theory.

Keywords

Complete Intersection Hyperplane Section Extremal Curve Rational Normal Curve Veronese Surface 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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Copyright information

© Springer Science+Business Media New York 1985

Authors and Affiliations

  • E. Arbarello
    • 1
  • M. Cornalba
    • 2
  • P. A. Griffiths
    • 3
  • J. Harris
    • 4
  1. 1.Dipartimento di Matematica, Istituto “Guido Castelnuovo”Università di Roma “La Sapienza”RomaItalia
  2. 2.Dipartimento di MatematicaUniversità di PaviaPaviaItalia
  3. 3.Office of the ProvostDuke UniversityDurhamUSA
  4. 4.Department of MathematicsBrown UniversityProvidenceUSA

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