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Article
Canonical Geometrically Ruled Surfaces
Matematische Nachrichten (2005)
  • Luis Fuentes García
  • Manuel Pedreira
Abstract

We prove the existence of canonical scrolls; that is, scrolls playing the role of canonical curves. First of all, they provide the geometrical version of Riemann Roch Theorem: any special scroll is the projection of a canonical scroll and they allow to understand the classification of special scrolls in PN. Canonical scrolls correspond to the projective model of canonical geometrically ruled surfaces over a smooth curve. We also prove that the generic canonical scroll is projectively normal except in the hyperelliptic case and for very particular cases in the nonhyperelliptic situation.

Keywords
  • Ruled surfaces; elementary trasnformation; projective normality
Disciplines
Publication Date
February, 2005
Citation Information
Luis Fuentes García and Manuel Pedreira. "Canonical Geometrically Ruled Surfaces" Matematische Nachrichten Vol. 278 (2005)
Available at: http://works.bepress.com/luis_fuentesgarcia/12/