The Dimension of the Hilbert Scheme of Special Threefolds

The Hilbert scheme of 3-folds in ℙ n , n ≥  6 , that are scrolls over ℙ 2 or over a smooth quadric surface Q  ⊂ ℙ 3 or that are quadric or cubic fibrations over ℙ 1 is studied. All known such threefolds of degree 7  ≤ d ≤  11 are shown to correspond to smooth points of an irreducible component of th...

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Bibliographic Details
Published in:Communications in algebra 2005-09, Vol.33 (10), p.3811-3829
Main Authors: Besana, Gian Mario, Fania, Maria Lucia
Format: Article
Language:English
Subjects:
Good determinantal subschemes
Hilbert schemes
Primary 14J30, 14M07, 14N25
Secondary 14N30
Special threefolds
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Summary:The Hilbert scheme of 3-folds in ℙ n , n ≥  6 , that are scrolls over ℙ 2 or over a smooth quadric surface Q  ⊂ ℙ 3 or that are quadric or cubic fibrations over ℙ 1 is studied. All known such threefolds of degree 7  ≤ d ≤  11 are shown to correspond to smooth points of an irreducible component of their Hilbert scheme, whose dimension is computed.
ISSN:0092-7872
1532-4125
DOI:10.1080/00927870500242926