Canonical Geometrically Ruled Surfaces

Details Canonical Geometrically Ruled Surfaces Canonical Geometrically Ruled Surfaces

2001-07-16

arxiv.org/abs/math/0107114v4

Mathematics

Algebraic Geometry

Latex2.09; 32 pages

Scientific paper

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 Teorem: any special scroll is the projection of a canonical scroll and they allow to understand the classification of special scrolls in P3. 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.

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