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The Basic Results of the Brill-Noether Theory

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

Abstract

As we recalled in Chapter I, a genus g curve depends on 3g — 3 parameters, describing the so-called moduli of the curve. Our goal in this chapter is to describe how the projective realizations of a curve vary with its moduli, and what it means, from this point of view, to say that a curve is “general” or “special.” Accordingly, we would like to know, first of all, what linear series can we expect to find on a general curve and, secondly, what the subvarieties of the moduli space corresponding to curves possessing linear series of specified type look like.

Keywords

Double Point General Curve Linear Series Smooth Plane Bibliographical Note 
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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