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Classification of smooth congruences of low degree

Arrondo Esteban, Enrique and Sols Lucía, 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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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
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:06 Feb 2014 10:10

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