%0 Journal Article
%A Arrondo Esteban, Enrique
%A Sols, Ignacio
%T Classification of smooth congruences of low degree
%D 1989
%@ 0075-4102
%U https://hdl.handle.net/20.500.14352/57185
%X We give a complete classification of smooth congruences - i.e. surfaces in the Grassmannvariety of lines in P 3C identified with a smooth quadric in P5- of degree at most 8, bystudying 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 linearnormality), as well as many information on the Hilbert scheme of these families, suchas dimension, smoothness, unirationality - and thus irreducibility - and in some casesrationality.
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