Classification of smooth congruences with a fundamental curve

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We give a classification and a construction of all smooth $(n-1)$-dimensional varieties of lines in ${\bf P}\sp n$ verifying that all their lines meet a curve. This also gives a complete classification of $(n-1)$-scrolls over a curve contained in $G(1,n)$.
Plain TeX, typeset by Textures 1.5, 13 pages

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