Two dimensional scrolls contained in quadric cones in ℙ5

Smooth, complex, ruled surfaces embedded in ℙ5 as linearly normal scrolls, such that they are contained in a quadric cone, are considered. Rational scrolls and some elliptic scrolls are shown to be the only ones contained in cones of rank 5. Results on scrolls contained in cones of lower ranks are a...

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Bibliographic Details
Published in:Abhandlungen aus dem Mathematischen Seminar der Universität Hamburg 2004-12, Vol.74 (1), p.57-75
Main Authors: Alzati, A., Bertolini, M., Besana, G.
Format: Article
Language:English
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Cones
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Summary:Smooth, complex, ruled surfaces embedded in ℙ5 as linearly normal scrolls, such that they are contained in a quadric cone, are considered. Rational scrolls and some elliptic scrolls are shown to be the only ones contained in cones of rank 5. Results on scrolls contained in cones of lower ranks are also obtained.
ISSN:0025-5858
1865-8784
DOI:10.1007/BF02941525