Canonical geometrically ruled surfaces
Copyright policy )Canonical geometrically ruled surfaces
AbstractWe 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. (© 2005 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)
Secondary, 14H25, 14H45, Mathematics - Algebraic Geometry, Coverings of curves, fundamental group, Special algebraic curves and curves of low genus, Primary, 14J26, Rational and ruled surfaces, elementary transformation, projective normality, FOS: Mathematics, Primary, 14J26; Secondary, 14H25, 14H45, Algebraic Geometry (math.AG)
Secondary, 14H25, 14H45, Mathematics - Algebraic Geometry, Coverings of curves, fundamental group, Special algebraic curves and curves of low genus, Primary, 14J26, Rational and ruled surfaces, elementary transformation, projective normality, FOS: Mathematics, Primary, 14J26; Secondary, 14H25, 14H45, Algebraic Geometry (math.AG)
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