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Canonical Geometrically Ruled Surfaces

Luis Fuentes Garcia·Manuel Pedreira Perez
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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 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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Luis Fuentes Garcia, Manuel Pedreira Perez. 2002-04-08. Canonical Geometrically Ruled Surfaces. https://arxiv.org/abs/math/0107114

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