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Arrondo Esteban, Enrique and Sols, Ignacio (1989) Classification of smooth congruences of low degree. Journal für die reine und angewandte Mathematik, 393 . pp. 199-219. ISSN 0075-4102
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Official URL: http://www.degruyter.com/view/j/crll
Abstract
We give a complete classification of smooth congruences - i.e. surfaces in the Grassmann
variety of lines in P 3C identified with a smooth quadric in P5- of degree at most 8, by
studying which surfaces of P5can lie in a smooth quadric and proving their existence.
We present their ideal sheaf as a quotient of natural bundles in the Grassmannian,
what provides a perfect knowledge of its cohomology (for example postulation or linear
normality), as well as many information on the Hilbert scheme of these families, such
as dimension, smoothness, unirationality - and thus irreducibility - and in some cases
rationality.
Item Type: | Article |
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Uncontrolled Keywords: | Smooth congruences; surfaces in the Grassmann variety of lines; cohomology; postulation; linear normality; Hilbert scheme |
Subjects: | Sciences > Mathematics > Algebraic geometry |
ID Code: | 14858 |
Deposited On: | 18 Apr 2012 10:37 |
Last Modified: | 22 Feb 2019 12:52 |
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