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Canonical geometrically ruled surfaces

✍ Scribed by Luis Fuentes García; Manuel Pedreira

Publisher
John Wiley and Sons
Year
2005
Tongue
English
Weight
243 KB
Volume
278
Category
Article
ISSN
0025-584X

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✦ Synopsis

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 P^N^. 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)

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